OEIS Similars: A154602
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A154602 | 1 1 1 3 4 1 11 19 9 1 49 104 70 16 1 257 641 550 190 25 1 1539 4380 4531 2080 425 36 1 10299 32803 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 1 1 4 3 1 9 19 11 1 16 70 104 49 1 25 190 550 641 257 1 36 425 2080 4531 4380 1539 1 49 833 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -4 1 -1 17 -9 1 1 -96 74 -16 1 -1 729 -690 210 -25 1 1 -7060 7579 -2840 475 -36 1 -1 83033 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -4 1 1 -9 17 -1 1 -16 74 -96 1 1 -25 210 -690 729 -1 1 -36 475 -2840 7579 -7060 1 1 -49 |
| Std | Accsee docs | missing | 1 1 2 3 7 8 11 30 39 40 49 153 223 239 240 257 898 1448 1638 1663 1664 1539 5919 10450 12530 12955 |
| Std | AccRevsee docs | missing | 1 1 2 1 5 8 1 10 29 40 1 17 87 191 240 1 26 216 766 1407 1664 1 37 462 2542 7073 11453 12992 1 50 |
| Std | AntiDiagsee docs | missing | 1 1 3 1 11 4 49 19 1 257 104 9 1539 641 70 1 10299 4380 550 16 75905 32803 4531 190 1 609441 266768 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 3 8 3 11 38 27 4 49 208 210 64 5 257 1282 1650 760 125 6 1539 8760 13593 8320 2125 216 7 |
| Std | RowSum∑ k=0..n T(n, k) | A055882 | 1 2 8 40 240 1664 12992 112256 1059840 10827264 118758400 1389711360 17258893312 226463227904 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 4 20 120 832 6496 56128 529920 5413632 59379200 694855680 8629446656 113231613952 1563847245824 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 4 20 120 832 6496 56128 529920 5413632 59379200 694855680 8629446656 113231613952 1563847245824 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A055882 | 1 2 8 40 240 1664 12992 112256 1059840 10827264 118758400 1389711360 17258893312 226463227904 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 4 15 69 370 2251 15245 113430 917829 8010197 74889352 745824909 7874454269 87779743900 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 18 120 904 7568 69376 689216 7361664 83996672 1018293760 13056668672 176379252736 2501793181696 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 14 80 536 4080 34560 321088 3236736 35103232 406807040 5009579008 65245253632 895155236864 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 12 1881 50960 1721501650 89999024637600 2559252346698100095 2696411135497225545898058560 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 19 104 641 4531 39515 365324 3575820 36971461 402741581 4991365808 65268062938 885442472096 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 4 19 70 550 2080 22491 87206 1192086 4719624 77684398 312957436 6009565276 24567605920 |
| Std | CentralET(2 n, n) | missing | 1 4 70 2080 87206 4719624 312957436 24567605920 2228251766598 229294798634616 26395503979168116 |
| Std | CentralOT(2 n + 1, n) | missing | 1 19 550 22491 1192086 77684398 6009565276 538271502483 54792517079014 6247940153497978 |
| Std | ColLeftT(n, 0) | A004211 | 1 1 3 11 49 257 1539 10299 75905 609441 5284451 49134923 487026929 5120905441 56878092067 |
| Std | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 12 96 950 10988 143976 2094032 33318534 573707692 10600961800 208798553824 4359572223292 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -4 20 -10 -776 7784 -25432 -416634 8540368 -72453016 -140179304 15367107260 -263768178480 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 6 40 296 2416 21568 208832 2176896 24275968 288048640 3619867648 47986360320 668692008960 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 14 80 536 4080 34560 321088 3236736 35103232 406807040 5009579008 65245253632 895155236864 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 8 64 544 4976 48960 516160 5804032 69305344 875277312 11649162240 162858278912 2384721481728 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 3 21 183 1929 23691 329565 5095551 86394513 1589803923 31491693093 667027338951 15023947341081 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A004213 | 1 -1 5 -29 201 -1657 15821 -170389 2032785 -26546673 376085653 -5736591885 93614616409 |
| Std | DiagRow1T(n + 1, n) | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Std | DiagRow2T(n + 2, n) | missing | 3 19 70 190 425 833 1484 2460 3855 5775 8338 11674 15925 21245 27800 35768 45339 56715 70110 85750 |
| Std | DiagRow3T(n + 3, n) | missing | 11 104 550 2080 6265 16016 36204 74400 141735 253880 432146 704704 1107925 1687840 2501720 3619776 |
| Std | DiagCol1T(n + 1, 1) | missing | 1 4 19 104 641 4380 32803 266768 2337505 21925236 218946003 2316939256 25878593313 304020964876 |
| Std | DiagCol2T(n + 2, 2) | missing | 1 9 70 550 4531 39515 365324 3575820 36971461 402741581 4610187154 55316069874 694067320311 |
| Std | DiagCol3T(n + 3, 3) | missing | 1 16 190 2080 22491 247072 2792476 32659840 396255541 4991365808 65268062938 885442472096 |
| Std | Polysee docs | missing | 1 1 1 3 2 1 11 8 3 1 49 40 15 4 1 257 240 93 24 5 1 1539 1664 681 176 35 6 1 10299 12992 5691 1504 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A005563 | 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 783 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 11 40 93 176 295 456 665 928 1251 1640 2101 2640 3263 3976 4785 5696 6715 7848 9101 10480 11991 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 3 15 93 681 5691 53079 544053 6058545 72652179 931542207 12697268205 183092096409 2781622021899 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A308543 | 1 4 24 176 1504 14528 155520 1819392 23019008 312413184 4518705152 69279690752 1120856170496 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 15 176 2865 59712 1517607 45521408 1574116353 61652866560 2697657422911 130420902973440 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A154602 | 1 1 -1 3 -4 1 11 -19 9 -1 49 -104 70 -16 1 257 -641 550 -190 25 -1 1539 -4380 4531 -2080 425 -36 1 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -4 3 -1 9 -19 11 1 -16 70 -104 49 -1 25 -190 550 -641 257 1 -36 425 -2080 4531 -4380 1539 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -7 4 1 33 -17 -9 1 865 -448 -214 16 1 -12403 6411 3090 -210 -25 1 -719695 372092 178939 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 4 -7 1 -9 -17 33 1 16 -214 -448 865 1 -25 -210 3090 6411 -12403 1 36 -1325 -12280 178939 |
| Alt | Accsee docs | missing | 1 1 0 3 -1 0 11 -8 1 0 49 -55 15 -1 0 257 -384 166 -24 1 0 1539 -2841 1690 -390 35 -1 0 10299 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -3 0 -1 8 -11 0 1 -15 55 -49 0 -1 24 -166 384 -257 0 1 -35 390 -1690 2841 -1539 0 -1 48 |
| Alt | AntiDiagsee docs | missing | 1 1 3 -1 11 -4 49 -19 1 257 -104 9 1539 -641 70 -1 10299 -4380 550 -16 75905 -32803 4531 -190 1 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 3 -8 3 11 -38 27 -4 49 -208 210 -64 5 257 -1282 1650 -760 125 -6 1539 -8760 13593 -8320 2125 |
| Alt | RowSum∑ k=0..n T(n, k) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 4 20 120 832 6496 56128 529920 5413632 59379200 694855680 8629446656 113231613952 1563847245824 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -4 -20 -120 -832 -6496 -56128 -529920 -5413632 -59379200 -694855680 -8629446656 -113231613952 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A055882 | 1 2 8 40 240 1664 12992 112256 1059840 10827264 118758400 1389711360 17258893312 226463227904 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A055882 | 1 2 8 40 240 1664 12992 112256 1059840 10827264 118758400 1389711360 17258893312 226463227904 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 7 31 162 967 6453 47444 380133 3290203 30544664 302346285 3175224045 35229483810 411445931955 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000079 | 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000079 | 1 -1 -2 -4 -8 -16 -32 -64 -128 -256 -512 -1024 -2048 -4096 -8192 -16384 -32768 -65536 -131072 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 12 1881 50960 1721501650 89999024637600 2559252346698100095 2696411135497225545898058560 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 19 104 641 4531 39515 365324 3575820 36971461 402741581 4991365808 65268062938 885442472096 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -4 -19 70 550 -2080 -22491 87206 1192086 -4719624 -77684398 312957436 6009565276 -24567605920 |
| Alt | CentralET(2 n, n) | missing | 1 -4 70 -2080 87206 -4719624 312957436 -24567605920 2228251766598 -229294798634616 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 -19 550 -22491 1192086 -77684398 6009565276 -538271502483 54792517079014 -6247940153497978 |
| Alt | ColLeftT(n, 0) | A004211 | 1 1 3 11 49 257 1539 10299 75905 609441 5284451 49134923 487026929 5120905441 56878092067 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 -20 -10 776 7784 25432 -416634 -8540368 -72453016 140179304 15367107260 263768178480 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 12 -96 950 -10988 143976 -2094032 33318534 -573707692 10600961800 -208798553824 4359572223292 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A000079 | 0 -1 -2 -4 -8 -16 -32 -64 -128 -256 -512 -1024 -2048 -4096 -8192 -16384 -32768 -65536 -131072 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A000079 | 1 -1 -2 -4 -8 -16 -32 -64 -128 -256 -512 -1024 -2048 -4096 -8192 -16384 -32768 -65536 -131072 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | A211012 | 0 -1 0 8 48 224 960 3968 16128 65024 261120 1046528 4190208 16769024 67092480 268402688 1073676288 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A004213 | 1 1 5 29 201 1657 15821 170389 2032785 26546673 376085653 5736591885 93614616409 1625661357673 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -3 21 -183 1929 -23691 329565 -5095551 86394513 -1589803923 31491693093 -667027338951 |
| Alt | DiagRow1T(n + 1, n) | A000290 | 1 -4 9 -16 25 -36 49 -64 81 -100 121 -144 169 -196 225 -256 289 -324 361 -400 441 -484 529 -576 625 |
| Alt | DiagRow2T(n + 2, n) | missing | 3 -19 70 -190 425 -833 1484 -2460 3855 -5775 8338 -11674 15925 -21245 27800 -35768 45339 -56715 |
| Alt | DiagRow3T(n + 3, n) | missing | 11 -104 550 -2080 6265 -16016 36204 -74400 141735 -253880 432146 -704704 1107925 -1687840 2501720 |
| Alt | DiagCol1T(n + 1, 1) | missing | -1 -4 -19 -104 -641 -4380 -32803 -266768 -2337505 -21925236 -218946003 -2316939256 -25878593313 |
| Alt | DiagCol2T(n + 2, 2) | missing | 1 9 70 550 4531 39515 365324 3575820 36971461 402741581 4610187154 55316069874 694067320311 |
| Alt | DiagCol3T(n + 3, 3) | missing | -1 -16 -190 -2080 -22491 -247072 -2792476 -32659840 -396255541 -4991365808 -65268062938 |
| Alt | Polysee docs | missing | 1 1 1 3 0 1 11 0 -1 1 49 0 -1 -2 1 257 0 1 0 -3 1 1539 0 9 8 3 -4 1 10299 0 23 16 15 8 -5 1 75905 0 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A005563 | 3 0 -1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 11 0 1 8 15 16 5 -24 -77 -160 -279 -440 -649 -912 -1235 -1624 -2085 -2624 -3247 -3960 -4769 -5680 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A009235 | 1 -1 -1 1 9 23 -25 -583 -3087 -4401 79087 902097 4783801 -2361049 -348382697 -4102879415 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A308536 | 1 -2 0 8 16 -64 -576 -1152 12800 136704 422912 -4464640 -72626176 -413966336 1805123584 64448004096 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -1 8 -15 -448 6615 -14208 -1213695 24336384 -25561809 -10091888640 241410805361 407872978944 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 1 1 4 3 1 9 19 11 1 16 70 104 49 1 25 190 550 641 257 1 36 425 2080 4531 4380 1539 1 49 833 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 1 -4 1 -1 17 -9 1 1 -96 74 -16 1 -1 729 -690 210 -25 1 1 -7060 7579 -2840 475 -36 1 -1 83033 |
| Rev | Accsee docs | missing | 1 1 2 1 5 8 1 10 29 40 1 17 87 191 240 1 26 216 766 1407 1664 1 37 462 2542 7073 11453 12992 1 50 |
| Rev | AccRevsee docs | missing | 1 1 2 3 7 8 11 30 39 40 49 153 223 239 240 257 898 1448 1638 1663 1664 1539 5919 10450 12530 12955 |
| Rev | AntiDiagsee docs | missing | 1 1 1 1 1 4 1 9 3 1 16 19 1 25 70 11 1 36 190 104 1 49 425 550 49 1 64 833 2080 641 1 81 1484 6265 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 8 9 1 18 57 44 1 32 210 416 245 1 50 570 2200 3205 1542 1 72 1275 8320 22655 26280 10773 1 |
| Rev | RowSum∑ k=0..n T(n, k) | A055882 | 1 2 8 40 240 1664 12992 112256 1059840 10827264 118758400 1389711360 17258893312 226463227904 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 4 20 120 832 6496 56128 529920 5413632 59379200 694855680 8629446656 113231613952 1563847245824 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 4 20 120 832 6496 56128 529920 5413632 59379200 694855680 8629446656 113231613952 1563847245824 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A055882 | 1 2 8 40 240 1664 12992 112256 1059840 10827264 118758400 1389711360 17258893312 226463227904 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 5 13 36 107 331 1074 3619 12619 45448 168441 641385 2504234 10008581 40893469 170585916 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 14 80 536 4080 34560 321088 3236736 35103232 406807040 5009579008 65245253632 895155236864 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 18 120 904 7568 69376 689216 7361664 83996672 1018293760 13056668672 176379252736 2501793181696 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 12 1881 50960 1721501650 89999024637600 2559252346698100095 2696411135497225545898058560 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 19 104 641 4531 39515 365324 3575820 36971461 402741581 4991365808 65268062938 885442472096 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 4 9 70 190 2080 6265 87206 281190 4719624 15982890 312957436 1100247148 24567605920 88980093345 |
| Rev | CentralET(2 n, n) | missing | 1 4 70 2080 87206 4719624 312957436 24567605920 2228251766598 229294798634616 26395503979168116 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 9 190 6265 281190 15982890 1100247148 88980093345 8269472552198 868501427798862 |
| Rev | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Rev | ColRightT(n, n) | A004211 | 1 1 3 11 49 257 1539 10299 75905 609441 5284451 49134923 487026929 5120905441 56878092067 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 12 96 950 10988 143976 2094032 33318534 573707692 10600961800 208798553824 4359572223292 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -4 -20 -10 776 7784 25432 -416634 -8540368 -72453016 140179304 15367107260 263768178480 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 10 80 664 5904 56384 576960 6301824 73169408 899535360 11666957312 159120359424 2275329953792 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 18 120 904 7568 69376 689216 7361664 83996672 1018293760 13056668672 176379252736 2501793181696 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 16 184 2016 22416 257856 3093056 38803456 509346304 6990144512 100167148544 1496466268160 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 3 15 93 681 5691 53079 544053 6058545 72652179 931542207 12697268205 183092096409 2781622021899 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A009235 | 1 -1 -1 1 9 23 -25 -583 -3087 -4401 79087 902097 4783801 -2361049 -348382697 -4102879415 |
| Rev | DiagRow1T(n + 1, n) | missing | 1 4 19 104 641 4380 32803 266768 2337505 21925236 218946003 2316939256 25878593313 304020964876 |
| Rev | DiagRow2T(n + 2, n) | missing | 1 9 70 550 4531 39515 365324 3575820 36971461 402741581 4610187154 55316069874 694067320311 |
| Rev | DiagRow3T(n + 3, n) | missing | 1 16 190 2080 22491 247072 2792476 32659840 396255541 4991365808 65268062938 885442472096 |
| Rev | DiagCol1T(n + 1, 1) | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Rev | DiagCol2T(n + 2, 2) | missing | 3 19 70 190 425 833 1484 2460 3855 5775 8338 11674 15925 21245 27800 35768 45339 56715 70110 85750 |
| Rev | DiagCol3T(n + 3, 3) | missing | 11 104 550 2080 6265 16016 36204 74400 141735 253880 432146 704704 1107925 1687840 2501720 3619776 |
| Rev | Polysee docs | missing | 1 1 1 1 2 1 1 8 3 1 1 40 21 4 1 1 240 183 40 5 1 1 1664 1929 496 65 6 1 1 12992 23691 7456 1045 96 |
| Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 |
| Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A000567 | 1 8 21 40 65 96 133 176 225 280 341 408 481 560 645 736 833 936 1045 1160 1281 1408 1541 1680 1825 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 40 183 496 1045 1896 3115 4768 6921 9640 12991 17040 21853 27496 34035 41536 50065 59688 70471 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 3 21 183 1929 23691 329565 5095551 86394513 1589803923 31491693093 667027338951 15023947341081 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 40 496 7456 131008 2613376 58038016 1415303680 37501484032 1070712260608 32716451246080 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 21 496 20385 1277376 112199437 13061229056 1937156666625 355391191221760 78810303550006501 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -4 1 -1 17 -9 1 1 -96 74 -16 1 -1 729 -690 210 -25 1 1 -7060 7579 -2840 475 -36 1 -1 83033 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -4 1 1 -9 17 -1 1 -16 74 -96 1 1 -25 210 -690 729 -1 1 -36 475 -2840 7579 -7060 1 1 -49 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 1 1 4 3 1 9 19 11 1 16 70 104 49 1 25 190 550 641 257 1 36 425 2080 4531 4380 1539 1 49 833 |
| Inv | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 -5 4 1 75 -59 -17 1 7553 -5944 -1706 96 1 -5453363 4291651 1231734 -69294 -729 1 |
| Inv | Accsee docs | missing | 1 -1 0 1 -3 -2 -1 16 7 8 1 -95 -21 -37 -36 -1 728 38 248 223 224 1 -7059 520 -2320 -1845 -1881 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -3 -2 1 -8 9 8 1 -15 59 -37 -36 1 -24 186 -504 225 224 1 -35 440 -2400 5179 -1881 -1880 1 |
| Inv | AntiDiagsee docs | missing | 1 -1 1 1 -1 -4 1 17 1 -1 -96 -9 1 729 74 1 -1 -7060 -690 -16 1 83033 7579 210 1 -1 -1146656 -97307 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 1 -8 3 -1 34 -27 4 1 -192 222 -64 5 -1 1458 -2070 840 -125 6 1 -14120 22737 -11360 2375 -216 |
| Inv | RowSum∑ k=0..n T(n, k) | A055142 | 1 0 -2 8 -36 224 -1880 19872 -251888 3712256 -62286624 1171487360 -24402416192 557542291968 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 2 -10 76 -716 8056 -106072 1604240 -27431056 523457056 -11029720736 254368729792 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -4 18 -112 940 -9936 125944 -1856128 31143312 -585743680 12201208096 -278771145984 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A084262 | 1 -2 6 -28 188 -1656 17992 -232016 3460368 -58574368 1109200736 -23230928832 533139875776 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A084262 | 1 2 6 28 188 1656 17992 232016 3460368 58574368 1109200736 23230928832 533139875776 13304094478208 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 2 -5 19 -106 805 -7767 90824 -1246829 19643613 -349194840 6912083749 -150747838597 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -4 30 -188 1460 -14464 175112 -2494512 40756592 -750182336 15348043744 -345356548800 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -4 10 -28 108 -576 3736 -24368 78224 2742848 -118708064 3722722112 -110898753344 3344119104000 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 153 3552 5868450 6496374713400 2674413767201758365 8381602311980946048 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 1 4 1 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 17 96 729 7579 97307 1436532 24010788 448512021 9263024749 209633261694 5159752220246 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -4 17 74 -690 -2840 41979 166054 -3370710 -13006392 336073562 1275590756 -40044216212 |
| Inv | CentralET(2 n, n) | missing | 1 -4 74 -2840 166054 -13006392 1275590756 -150231628976 20649462986438 -3244340330395736 |
| Inv | CentralOT(2 n + 1, n) | missing | -1 17 -690 41979 -3370710 336073562 -40044216212 5551818806963 -878088454231846 156041241001898174 |
| Inv | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -6 24 -2 -1280 21436 -278768 2992326 -17511744 -391589412 22121578512 -738807000788 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 10 80 894 12772 220188 4418864 100793542 2568997340 72233184316 2218158930176 73792960032300 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 -2 2 8 -116 1304 -16136 227520 -3634032 65029472 -1290195424 28125138304 -668441045312 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -4 10 -28 108 -576 3736 -24368 78224 2742848 -118708064 3722722112 -110898753344 3344119104000 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 0 -10 72 -516 4432 -46264 573248 -8228592 134240384 -2452463520 49592005504 -1099501147200 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 -3 43 -487 6903 -125483 2805731 -74339151 2273625199 -78771713491 3047750237211 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 3 13 95 1113 18107 371941 9173271 263542705 8636905331 317864233149 12977209598927 |
| Inv | DiagRow1T(n + 1, n) | A000290 | -1 -4 -9 -16 -25 -36 -49 -64 -81 -100 -121 -144 -169 -196 -225 -256 -289 -324 -361 -400 -441 -484 |
| Inv | DiagRow2T(n + 2, n) | missing | 1 17 74 210 475 931 1652 2724 4245 6325 9086 12662 17199 22855 29800 38216 48297 60249 74290 90650 |
| Inv | DiagRow3T(n + 3, n) | missing | -1 -96 -690 -2840 -8715 -22176 -49476 -100080 -187605 -330880 -555126 -893256 -1387295 -2089920 |
| Inv | DiagCol1T(n + 1, 1) | A353546 | 1 -4 17 -96 729 -7060 83033 -1146656 18164625 -324488068 6450956929 -141233271872 3376008830505 |
| Inv | DiagCol2T(n + 2, 2) | missing | 1 -9 74 -690 7579 -97307 1436532 -24010788 448512021 -9263024749 209633261694 -5159752220246 |
| Inv | DiagCol3T(n + 3, 3) | missing | 1 -16 210 -2840 41979 -687232 12447812 -248149040 5410685621 -128249515152 3286014685590 |
| Inv | Polysee docs | missing | 1 -1 1 1 0 1 -1 -2 1 1 1 8 -3 2 1 -1 -36 5 -2 3 1 1 224 -7 -4 1 4 1 -1 -1880 9 28 -13 6 5 1 1 19872 |
| Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 |
| Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A123968 | 1 -2 -3 -2 1 6 13 22 33 46 61 78 97 118 141 166 193 222 253 286 321 358 397 438 481 526 573 622 673 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -1 8 5 -4 -13 -16 -7 20 71 152 269 428 635 896 1217 1604 2063 2600 3221 3932 4739 5648 6665 7796 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A005408 | 1 1 -3 5 -7 9 -11 13 -15 17 -19 21 -23 25 -27 29 -31 33 -35 37 -39 41 -43 45 -47 49 -51 53 -55 57 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 -2 -4 28 -136 808 -6448 66064 -821728 11958496 -198818368 3713280448 -76920529024 1749547404928 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -3 -4 33 144 -635 -6672 17409 432512 -618579 -40015680 26978017 5267018496 -1393988427 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -4 1 1 -9 17 -1 1 -16 74 -96 1 1 -25 210 -690 729 -1 1 -36 475 -2840 7579 -7060 1 1 -49 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -4 1 -1 17 -9 1 1 -96 74 -16 1 -1 729 -690 210 -25 1 1 -7060 7579 -2840 475 -36 1 -1 83033 |
| Inv:Rev | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -5 4 1 75 -59 -17 1 7553 -5944 -1706 96 1 -5453363 4291651 1231734 -69294 -729 1 |
| Inv:Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 4 -5 1 -17 -59 75 1 96 -1706 -5944 7553 1 -729 -69294 1231734 4291651 -5453363 1 7060 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A154602 | 1 1 1 3 4 1 11 19 9 1 49 104 70 16 1 257 641 550 190 25 1 1539 4380 4531 2080 425 36 1 10299 32803 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -3 -2 1 -8 9 8 1 -15 59 -37 -36 1 -24 186 -504 225 224 1 -35 440 -2400 5179 -1881 -1880 1 |
| Inv:Rev | AccRevsee docs | missing | 1 -1 0 1 -3 -2 -1 16 7 8 1 -95 -21 -37 -36 -1 728 38 248 223 224 1 -7059 520 -2320 -1845 -1881 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -4 1 -9 1 1 -16 17 1 -25 74 -1 1 -36 210 -96 1 -49 475 -690 1 1 -64 931 -2840 729 1 -81 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -8 3 1 -18 51 -4 1 -32 222 -384 5 1 -50 630 -2760 3645 -6 1 -72 1425 -11360 37895 -42360 7 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A055142 | 1 0 -2 8 -36 224 -1880 19872 -251888 3712256 -62286624 1171487360 -24402416192 557542291968 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 2 18 76 940 8056 125944 1604240 31143312 523457056 12201208096 254368729792 6930818385088 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -4 -10 -112 -716 -9936 -106072 -1856128 -27431056 -585743680 -11029720736 -278771145984 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A084262 | 1 2 6 28 188 1656 17992 232016 3460368 58574368 1109200736 23230928832 533139875776 13304094478208 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A084262 | 1 2 6 28 188 1656 17992 232016 3460368 58574368 1109200736 23230928832 533139875776 13304094478208 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -3 -7 2 49 79 -262 -1243 435 15368 23397 -169947 -674408 1462009 14436085 853010 -279329147 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -4 10 -28 108 -576 3736 -24368 78224 2742848 -118708064 3722722112 -110898753344 3344119104000 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -4 30 -188 1460 -14464 175112 -2494512 40756592 -750182336 15348043744 -345356548800 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 153 3552 5868450 6496374713400 2674413767201758365 8381602311980946048 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 1 4 1 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 17 96 729 7579 97307 1436532 24010788 448512021 9263024749 209633261694 5159752220246 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -4 -9 74 210 -2840 -8715 166054 528150 -13006392 -42224490 1275590756 4196756564 -150231628976 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 -4 74 -2840 166054 -13006392 1275590756 -150231628976 20649462986438 -3244340330395736 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -9 210 -8715 528150 -42224490 4196756564 -498945642195 69063422294438 -10910079074278670 |
| Inv:Rev | ColLeftT(n, 0) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -6 24 -2 -1280 21436 -278768 2992326 -17511744 -391589412 22121578512 -738807000788 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 10 -80 894 -12772 220188 -4418864 100793542 -2568997340 72233184316 -2218158930176 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 -2 22 -152 1236 -12584 155240 -2242624 37044336 -687895712 14176556384 -320954132608 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -4 30 -188 1460 -14464 175112 -2494512 40756592 -750182336 15348043744 -345356548800 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 0 50 -568 6244 -78896 1153368 -19187904 357876720 -7395011456 167681806368 -4139359245440 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A005408 | 1 1 -3 5 -7 9 -11 13 -15 17 -19 21 -23 25 -27 29 -31 33 -35 37 -39 41 -43 45 -47 49 -51 53 -55 57 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A010844 | 1 -3 13 -79 633 -6331 75973 -1063623 17017969 -306323443 6126468861 -134782314943 3234775558633 |
| Inv:Rev | DiagRow1T(n + 1, n) | A353546 | 1 -4 17 -96 729 -7060 83033 -1146656 18164625 -324488068 6450956929 -141233271872 3376008830505 |
| Inv:Rev | DiagRow2T(n + 2, n) | missing | 1 -9 74 -690 7579 -97307 1436532 -24010788 448512021 -9263024749 209633261694 -5159752220246 |
| Inv:Rev | DiagRow3T(n + 3, n) | missing | 1 -16 210 -2840 41979 -687232 12447812 -248149040 5410685621 -128249515152 3286014685590 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A000290 | -1 -4 -9 -16 -25 -36 -49 -64 -81 -100 -121 -144 -169 -196 -225 -256 -289 -324 -361 -400 -441 -484 |
| Inv:Rev | DiagCol2T(n + 2, 2) | missing | 1 17 74 210 475 931 1652 2724 4245 6325 9086 12662 17199 22855 29800 38216 48297 60249 74290 90650 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | -1 -96 -690 -2840 -8715 -22176 -49476 -100080 -187605 -330880 -555126 -893256 -1387295 -2089920 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 -2 -1 1 1 8 -3 -2 1 1 -36 43 -2 -3 1 1 224 -487 100 1 -4 1 1 -1880 6903 -1892 173 6 |
| Inv:Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 |
| Inv:Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A123968 | 1 -2 -3 -2 1 6 13 22 33 46 61 78 97 118 141 166 193 222 253 286 321 358 397 438 481 526 573 622 673 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 8 43 100 173 256 343 428 505 568 611 628 613 560 463 316 113 -152 -485 -892 -1379 -1952 -2617 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -1 -3 43 -487 6903 -125483 2805731 -74339151 2273625199 -78771713491 3047750237211 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 -2 100 -1892 41992 -1173464 40056496 -1614629360 74963332576 -3936376667936 230561953548352 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -3 100 -4767 371376 -45626075 8230334736 -2049967211775 673503972300928 -282046130324276499 |
| << | Table | Source | Similars | Index | >> |
Note: The A-numbers are based on a finite number of numerical comparisons. They ignore the sign and the OEIS-offset. Sometimes they differ in the first few values. In such cases, we consider our version to be the better one because it has a common formula as a root. Since the offset of all triangles is 0 also the offset of all sequences is 0.