OEIS Similars: A104684, A063007
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A104684 | 1 2 1 6 6 1 20 30 12 1 70 140 90 20 1 252 630 560 210 30 1 924 2772 3150 1680 420 42 1 3432 12012 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A063007 | 1 1 2 1 6 6 1 12 30 20 1 20 90 140 70 1 30 210 560 630 252 1 42 420 1680 3150 2772 924 1 56 756 |
| Std | Accsee docs | missing | 1 2 3 6 12 13 20 50 62 63 70 210 300 320 321 252 882 1442 1652 1682 1683 924 3696 6846 8526 8946 |
| Std | AccRevsee docs | missing | 1 1 3 1 7 13 1 13 43 63 1 21 111 251 321 1 31 241 801 1431 1683 1 43 463 2143 5293 8065 8989 1 57 |
| Std | AntiDiagsee docs | missing | 1 2 6 1 20 6 70 30 1 252 140 12 924 630 90 1 3432 2772 560 20 12870 12012 3150 210 1 48620 51480 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 2 2 6 12 3 20 60 36 4 70 280 270 80 5 252 1260 1680 840 150 6 924 5544 9450 6720 2100 252 7 3432 |
| Std | RowSum∑ k=0..n T(n, k) | A001850 | 1 3 13 63 321 1683 8989 48639 265729 1462563 8097453 45046719 251595969 1409933619 7923848253 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A226994 | 1 2 7 32 161 842 4495 24320 132865 731282 4048727 22523360 125797985 704966810 3961924127 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A047665 | 0 1 6 31 160 841 4494 24319 132864 731281 4048726 22523359 125797984 704966809 3961924126 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | 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 | AbsSum∑ k=0..n | T(n, k) | | A001850 | 1 3 13 63 321 1683 8989 48639 265729 1462563 8097453 45046719 251595969 1409933619 7923848253 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A349713 | 1 2 7 26 101 404 1645 6784 28243 118442 499601 2117366 9008969 38458644 164643197 706574780 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 5 31 195 1221 7593 46915 288263 1762825 10736973 65171943 394414155 2380819533 14339099505 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 4 21 120 705 4188 24997 149488 894465 5351220 31997493 191193192 1141524033 6809904780 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 6 60 1260 5040 277200 5405400 12612600 343062720 58663725120 48886437600 12368268712800 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 2 6 2 10 2 42 2 6 2 22 2 26 2 2 2 34 2 114 2 30 2 46 2 30 2 6 2 58 2 62 2 2 2 2 2 74 2 2 2 82 2 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 2 6 30 140 630 3150 16632 84084 420420 2333760 12471030 64664600 355655300 1963217256 10546208400 |
| Std | ColMiddleT(n, n // 2) | missing | 1 2 6 30 90 560 1680 11550 34650 252252 756756 5717712 17153136 133024320 399072960 3155170590 |
| Std | CentralET(2 n, n) | A006480 | 1 6 90 1680 34650 756756 17153136 399072960 9465511770 227873431500 5550996791340 136526995463040 |
| Std | CentralOT(2 n + 1, n) | A208881 | 2 30 560 11550 252252 5717712 133024320 3155170590 75957810500 1850332263780 45508998487680 |
| Std | ColLeftT(n, 0) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| 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) | A005258 | 1 3 19 147 1251 11253 104959 1004307 9793891 96918753 970336269 9807518757 99912156111 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -1 -5 35 -29 -751 3991 4115 -137885 495269 2114245 -25786795 50109775 627370925 -4643568305 |
| Std | TransNat0∑ k=0..n T(n, k) k | A108666 | 0 1 8 57 384 2505 16008 100849 628736 3888657 23900040 146146473 889928064 5399971161 32668236552 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 4 21 120 705 4188 24997 149488 894465 5351220 31997493 191193192 1141524033 6809904780 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 10 87 696 5265 38298 270655 1870816 12706353 85078170 562969143 3688327800 23959844961 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A006442 | 1 5 37 305 2641 23525 213445 1961825 18205345 170195525 1600472677 15122515985 143457011569 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001850 | 1 -3 13 -63 321 -1683 8989 -48639 265729 -1462563 8097453 -45046719 251595969 -1409933619 |
| Std | DiagRow1T(n + 1, n) | A002378 | 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
| Std | DiagRow2T(n + 2, n) | A033487 | 6 30 90 210 420 756 1260 1980 2970 4290 6006 8190 10920 14280 18360 23256 29070 35910 43890 53130 |
| Std | DiagRow3T(n + 3, n) | A105939 | 20 140 560 1680 4200 9240 18480 34320 60060 100100 160160 247520 371280 542640 775200 1085280 |
| Std | DiagCol1T(n + 1, 1) | A002457 | 1 6 30 140 630 2772 12012 51480 218790 923780 3879876 16224936 67603900 280816200 1163381400 |
| Std | DiagCol2T(n + 2, 2) | A002544 | 1 12 90 560 3150 16632 84084 411840 1969110 9237800 42678636 194699232 878850700 3931426800 |
| Std | DiagCol3T(n + 3, 3) | A007744 | 1 20 210 1680 11550 72072 420420 2333760 12471030 64664600 327202876 1622493600 7909656300 |
| Std | Polysee docs | missing | 1 2 1 6 3 1 20 13 4 1 70 63 22 5 1 252 321 136 33 6 1 924 1683 886 245 46 7 1 3432 8989 5944 1921 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 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 37 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A028872 | 6 13 22 33 46 61 78 97 118 141 166 193 222 253 286 321 358 397 438 481 526 573 622 673 726 781 838 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 20 63 136 245 396 595 848 1161 1540 1991 2520 3133 3836 4635 5536 6545 7668 8911 10280 11781 13420 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A069835 | 1 4 22 136 886 5944 40636 281488 1968934 13875544 98365972 700701808 5011371964 35961808432 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A084771 | 1 5 33 245 1921 15525 127905 1067925 9004545 76499525 653808673 5614995765 48416454529 418895174885 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A335309 | 1 3 22 245 3606 65527 1411404 35066313 985483270 30869546411 1065442493556 40144438269949 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A104684 | 1 2 -1 6 -6 1 20 -30 12 -1 70 -140 90 -20 1 252 -630 560 -210 30 -1 924 -2772 3150 -1680 420 -42 1 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A063007 | 1 -1 2 1 -6 6 -1 12 -30 20 1 -20 90 -140 70 -1 30 -210 560 -630 252 1 -42 420 -1680 3150 -2772 924 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -2 1 -18 6 1 136 -42 -12 1 3990 -1240 -330 20 1 -82572 25650 6820 -390 -30 1 -4865112 1511412 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -2 1 6 -18 1 -12 -42 136 1 20 -330 -1240 3990 1 -30 -390 6820 25650 -82572 1 42 -1680 -23100 |
| Alt | Accsee docs | missing | 1 2 1 6 0 1 20 -10 2 1 70 -70 20 0 1 252 -378 182 -28 2 1 924 -1848 1302 -378 42 0 1 3432 -8580 |
| Alt | AccRevsee docs | missing | 1 -1 1 1 -5 1 -1 11 -19 1 1 -19 71 -69 1 -1 29 -181 379 -251 1 1 -41 379 -1301 1849 -923 1 -1 55 |
| Alt | AntiDiagsee docs | missing | 1 2 6 -1 20 -6 70 -30 1 252 -140 12 924 -630 90 -1 3432 -2772 560 -20 12870 -12012 3150 -210 1 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 2 -2 6 -12 3 20 -60 36 -4 70 -280 270 -80 5 252 -1260 1680 -840 150 -6 924 -5544 9450 -6720 2100 |
| Alt | RowSum∑ k=0..n T(n, k) | 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 | EvenSum∑ k=0..n T(n, k) even(k) | A226994 | 1 2 7 32 161 842 4495 24320 132865 731282 4048727 22523360 125797985 704966810 3961924127 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A047665 | 0 -1 -6 -31 -160 -841 -4494 -24319 -132864 -731281 -4048726 -22523359 -125797984 -704966809 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A001850 | 1 3 13 63 321 1683 8989 48639 265729 1462563 8097453 45046719 251595969 1409933619 7923848253 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A001850 | 1 3 13 63 321 1683 8989 48639 265729 1462563 8097453 45046719 251595969 1409933619 7923848253 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A108626 | 1 2 5 14 41 124 383 1200 3799 12122 38919 125578 406865 1322772 4313155 14099524 46192483 151628090 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A002061 | 1 3 7 13 21 31 43 57 73 91 111 133 157 183 211 241 273 307 343 381 421 463 507 553 601 651 703 757 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A005563 | 1 0 -3 -8 -15 -24 -35 -48 -63 -80 -99 -120 -143 -168 -195 -224 -255 -288 -323 -360 -399 -440 -483 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 6 60 1260 5040 277200 5405400 12612600 343062720 58663725120 48886437600 12368268712800 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 2 6 2 10 2 42 2 6 2 22 2 26 2 2 2 34 2 114 2 30 2 46 2 30 2 6 2 58 2 62 2 2 2 2 2 74 2 2 2 82 2 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 2 6 30 140 630 3150 16632 84084 420420 2333760 12471030 64664600 355655300 1963217256 10546208400 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 2 -6 -30 90 560 -1680 -11550 34650 252252 -756756 -5717712 17153136 133024320 -399072960 |
| Alt | CentralET(2 n, n) | A006480 | 1 -6 90 -1680 34650 -756756 17153136 -399072960 9465511770 -227873431500 5550996791340 |
| Alt | CentralOT(2 n + 1, n) | A208881 | 2 -30 560 -11550 252252 -5717712 133024320 -3155170590 75957810500 -1850332263780 45508998487680 |
| Alt | ColLeftT(n, 0) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 1 -5 -35 -29 751 3991 -4115 -137885 -495269 2114245 25786795 50109775 -627370925 -4643568305 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A005258 | 1 -3 19 -147 1251 -11253 104959 -1004307 9793891 -96918753 970336269 -9807518757 99912156111 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A000290 | 0 -1 -4 -9 -16 -25 -36 -49 -64 -81 -100 -121 -144 -169 -196 -225 -256 -289 -324 -361 -400 -441 -484 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A005563 | 1 0 -3 -8 -15 -24 -35 -48 -63 -80 -99 -120 -143 -168 -195 -224 -255 -288 -323 -360 -399 -440 -483 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 -2 9 56 175 414 833 1504 2511 3950 5929 8568 11999 16366 21825 28544 36703 46494 58121 71800 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A001850 | 1 3 13 63 321 1683 8989 48639 265729 1462563 8097453 45046719 251595969 1409933619 7923848253 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A006442 | 1 -5 37 -305 2641 -23525 213445 -1961825 18205345 -170195525 1600472677 -15122515985 143457011569 |
| Alt | DiagRow1T(n + 1, n) | A002378 | 2 -6 12 -20 30 -42 56 -72 90 -110 132 -156 182 -210 240 -272 306 -342 380 -420 462 -506 552 -600 |
| Alt | DiagRow2T(n + 2, n) | A033487 | 6 -30 90 -210 420 -756 1260 -1980 2970 -4290 6006 -8190 10920 -14280 18360 -23256 29070 -35910 |
| Alt | DiagRow3T(n + 3, n) | A105939 | 20 -140 560 -1680 4200 -9240 18480 -34320 60060 -100100 160160 -247520 371280 -542640 775200 |
| Alt | DiagCol1T(n + 1, 1) | A002457 | -1 -6 -30 -140 -630 -2772 -12012 -51480 -218790 -923780 -3879876 -16224936 -67603900 -280816200 |
| Alt | DiagCol2T(n + 2, 2) | A002544 | 1 12 90 560 3150 16632 84084 411840 1969110 9237800 42678636 194699232 878850700 3931426800 |
| Alt | DiagCol3T(n + 3, 3) | A007744 | -1 -20 -210 -1680 -11550 -72072 -420420 -2333760 -12471030 -64664600 -327202876 -1622493600 |
| Alt | Polysee docs | missing | 1 2 1 6 1 1 20 1 0 1 70 1 -2 -1 1 252 1 0 -3 -2 1 924 1 6 11 -2 -3 1 3432 1 0 1 28 1 -4 1 12870 1 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 2 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 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | missing | 6 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 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 20 1 0 11 28 45 56 55 36 -7 -80 -189 -340 -539 -792 -1105 -1484 -1935 -2464 -3077 -3780 -4579 -5480 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A126869 | 1 0 -2 0 6 0 -20 0 70 0 -252 0 924 0 -3432 0 12870 0 -48620 0 184756 0 -705432 0 2704156 0 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A098332 | 1 -1 -3 11 1 -81 141 363 -1791 479 13597 -29877 -54911 353807 -223443 -2539989 6806529 8302527 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A335310 | 1 1 -2 11 -74 477 -804 -84425 3315334 -102211207 3005297956 -88338323709 2627003399164 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A063007 | 1 1 2 1 6 6 1 12 30 20 1 20 90 140 70 1 30 210 560 630 252 1 42 420 1680 3150 2772 924 1 56 756 |
| Rev | Accsee docs | missing | 1 1 3 1 7 13 1 13 43 63 1 21 111 251 321 1 31 241 801 1431 1683 1 43 463 2143 5293 8065 8989 1 57 |
| Rev | AccRevsee docs | missing | 1 2 3 6 12 13 20 50 62 63 70 210 300 320 321 252 882 1442 1652 1682 1683 924 3696 6846 8526 8946 |
| Rev | AntiDiagsee docs | missing | 1 1 1 2 1 6 1 12 6 1 20 30 1 30 90 20 1 42 210 140 1 56 420 560 70 1 72 756 1680 630 1 90 1260 4200 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 4 1 12 18 1 24 90 80 1 40 270 560 350 1 60 630 2240 3150 1512 1 84 1260 6720 15750 16632 6468 1 |
| Rev | RowSum∑ k=0..n T(n, k) | A001850 | 1 3 13 63 321 1683 8989 48639 265729 1462563 8097453 45046719 251595969 1409933619 7923848253 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 7 31 161 841 4495 24319 132865 731281 4048727 22523359 125797985 704966809 3961924127 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 2 6 32 160 842 4494 24320 132864 731282 4048726 22523360 125797984 704966810 3961924126 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A001850 | 1 3 13 63 321 1683 8989 48639 265729 1462563 8097453 45046719 251595969 1409933619 7923848253 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A002426 | 1 1 3 7 19 51 141 393 1107 3139 8953 25653 73789 212941 616227 1787607 5196627 15134931 44152809 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 4 21 120 705 4188 24997 149488 894465 5351220 31997493 191193192 1141524033 6809904780 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 5 31 195 1221 7593 46915 288263 1762825 10736973 65171943 394414155 2380819533 14339099505 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 6 60 1260 5040 277200 5405400 12612600 343062720 58663725120 48886437600 12368268712800 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 2 6 2 10 2 42 2 6 2 22 2 26 2 2 2 34 2 114 2 30 2 46 2 30 2 6 2 58 2 62 2 2 2 2 2 74 2 2 2 82 2 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 2 6 30 140 630 3150 16632 84084 420420 2333760 12471030 64664600 355655300 1963217256 10546208400 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 6 12 90 210 1680 4200 34650 90090 756756 2018016 17153136 46558512 399072960 1097450640 |
| Rev | CentralET(2 n, n) | A006480 | 1 6 90 1680 34650 756756 17153136 399072960 9465511770 227873431500 5550996791340 136526995463040 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 12 210 4200 90090 2018016 46558512 1097450640 26293088250 638045608200 15643718230140 |
| 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) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A005258 | 1 3 19 147 1251 11253 104959 1004307 9793891 96918753 970336269 9807518757 99912156111 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 1 -5 -35 -29 751 3991 -4115 -137885 -495269 2114245 25786795 50109775 -627370925 -4643568305 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 2 18 132 900 5910 37926 239624 1497096 9274410 57074490 349367436 2129223564 12929165886 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 5 31 195 1221 7593 46915 288263 1762825 10736973 65171943 394414155 2380819533 14339099505 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 2 30 312 2760 22290 169806 1242080 8817696 61178130 416822670 2798399736 18559873800 121839376386 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A069835 | 1 4 22 136 886 5944 40636 281488 1968934 13875544 98365972 700701808 5011371964 35961808432 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A126869 | 1 0 -2 0 6 0 -20 0 70 0 -252 0 924 0 -3432 0 12870 0 -48620 0 184756 0 -705432 0 2704156 0 |
| Rev | DiagRow1T(n + 1, n) | A002457 | 1 6 30 140 630 2772 12012 51480 218790 923780 3879876 16224936 67603900 280816200 1163381400 |
| Rev | DiagRow2T(n + 2, n) | A002544 | 1 12 90 560 3150 16632 84084 411840 1969110 9237800 42678636 194699232 878850700 3931426800 |
| Rev | DiagRow3T(n + 3, n) | A007744 | 1 20 210 1680 11550 72072 420420 2333760 12471030 64664600 327202876 1622493600 7909656300 |
| Rev | DiagCol1T(n + 1, 1) | A002378 | 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756 |
| Rev | DiagCol2T(n + 2, 2) | A033487 | 6 30 90 210 420 756 1260 1980 2970 4290 6006 8190 10920 14280 18360 23256 29070 35910 43890 53130 |
| Rev | DiagCol3T(n + 3, 3) | A105939 | 20 140 560 1680 4200 9240 18480 34320 60060 100100 160160 247520 371280 542640 775200 1085280 |
| Rev | Polysee docs | missing | 1 1 1 1 3 1 1 13 5 1 1 63 37 7 1 1 321 305 73 9 1 1 1683 2641 847 121 11 1 1 8989 23525 10321 1809 |
| Rev | PolyRow1∑ k=0..1 T(1, k) n^k | A005408 | 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 59 61 63 65 67 69 |
| Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A003154 | 1 13 37 73 121 181 253 337 433 541 661 793 937 1093 1261 1441 1633 1837 2053 2281 2521 2773 3037 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | A160674 | 1 63 305 847 1809 3311 5473 8415 12257 17119 23121 30383 39025 49167 60929 74431 89793 107135 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A006442 | 1 5 37 305 2641 23525 213445 1961825 18205345 170195525 1600472677 15122515985 143457011569 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A084768 | 1 7 73 847 10321 129367 1651609 21360031 278905249 3668760487 48543499753 645382441711 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A331656 | 1 3 37 847 28401 1256651 69125869 4548342975 348434664769 30463322582899 2993348092318101 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A063007 | 1 1 2 1 6 6 1 12 30 20 1 20 90 140 70 1 30 210 560 630 252 1 42 420 1680 3150 2772 924 1 56 756 |
| Inv | Accsee docs | missing | 1 -2 -1 6 0 1 -32 10 -2 -1 310 -130 20 0 1 -4932 2178 -362 28 -2 -1 116424 -51828 8862 -798 42 0 1 |
| Inv | AccRevsee docs | missing | 1 1 -1 1 -5 1 1 -11 31 -1 1 -19 131 -309 1 1 -29 361 -2179 4931 -1 1 -41 799 -8861 51829 -116423 1 |
| Inv | AntiDiagsee docs | missing | 1 -2 6 1 -32 -6 310 42 1 -4932 -440 -12 116424 7110 150 1 -3802752 -168252 -2540 -20 163825974 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -2 2 6 -12 3 -32 84 -36 4 310 -880 450 -80 5 -4932 14220 -7620 1560 -150 6 116424 -336504 182070 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -2 7 -44 461 -7502 177955 -5817800 250675801 -13754614922 935751981407 -77267496160340 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -6 43 -460 7501 -177954 5817799 -250675800 13754614921 -935751981406 77267496160339 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -3 13 -87 921 -15003 355909 -11635599 501351601 -27509229843 1871503962813 -154534992320679 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 3 13 87 921 15003 355909 11635599 501351601 27509229843 1871503962813 154534992320679 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -2 7 -38 353 -5384 123685 -3973564 169384687 -9227759606 624611157821 -51384379710446 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -3 7 -25 201 -3091 72703 -2373897 102265705 -5611148011 381734646591 -31520799931633 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 0 -3 20 -195 3084 -72695 2373888 -102265695 5611148000 -381734646579 31520799931620 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 6 672 204600 3216379140 7750311334920 131426737497966879360 54722432423401919925487384726080 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 2 6 2 10 2 42 2 6 2 22 2 26 2 2 2 34 2 114 2 30 2 46 2 30 2 6 2 58 2 62 2 2 2 2 2 74 2 2 2 82 2 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 2 6 42 440 7110 168252 5497632 236856384 12996105750 884146372340 73006244474196 7190633348844816 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -2 -6 42 150 -2540 -9660 318570 1240470 -68166252 -268199316 22151452092 87622410876 |
| Inv | CentralET(2 n, n) | missing | 1 -6 150 -9660 1240470 -268199316 87622410876 -40261266559800 24737671557915030 |
| Inv | CentralOT(2 n + 1, n) | missing | -2 42 -2540 318570 -68166252 22151452092 -10146680307192 6222162826878570 -4918371152543308460 |
| Inv | ColLeftT(n, 0) | missing | 1 -2 6 -32 310 -4932 116424 -3802752 163825974 -8988907100 611529126076 -50495522176992 |
| 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 -1 -5 59 -629 8969 -163589 3149075 -21014069 -5852034211 899181599845 -115896134963995 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 3 19 195 3051 69933 2242339 96184707 5316455755 367541743353 31038259817709 3141413180151117 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 -4 21 -196 3085 -72696 2373889 -102265696 5611148001 -381734646580 31520799931621 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 0 -3 20 -195 3084 -72695 2373888 -102265695 5611148000 -381734646579 31520799931620 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | A000027 | 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 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -3 13 -111 2001 -62883 2964109 -193594719 16680002593 -1830409796163 249050983487373 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 5 37 449 9121 293525 13886965 907498625 78196256065 8581126634405 1167576334672837 |
| Inv | DiagRow1T(n + 1, n) | A002378 | -2 -6 -12 -20 -30 -42 -56 -72 -90 -110 -132 -156 -182 -210 -240 -272 -306 -342 -380 -420 -462 -506 |
| Inv | DiagRow2T(n + 2, n) | missing | 6 42 150 390 840 1596 2772 4500 6930 10230 14586 20202 27300 36120 46920 59976 75582 94050 115710 |
| Inv | DiagRow3T(n + 3, n) | missing | -32 -440 -2540 -9660 -28560 -71232 -157080 -315480 -588720 -1035320 -1733732 -2786420 -4324320 |
| Inv | DiagCol1T(n + 1, 1) | missing | 1 -6 42 -440 7110 -168252 5497632 -236856384 12996105750 -884146372340 73006244474196 |
| Inv | DiagCol2T(n + 2, 2) | missing | 1 -12 150 -2540 60690 -1986432 85606584 -4697384400 319573375110 -26388034855160 2599047970783836 |
| Inv | DiagCol3T(n + 3, 3) | missing | 1 -20 390 -9660 318570 -13748112 754567800 -51337094160 4239074011590 -417521481514280 |
| Inv | Polysee docs | missing | 1 -2 1 6 -1 1 -32 1 0 1 310 -1 -2 1 1 -4932 1 12 -3 2 1 116424 -1 -114 13 -2 3 1 -3802752 1 1800 |
| Inv | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | -2 -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 |
| Inv | PolyRow2∑ k=0..2 T(2, k) n^k | missing | 6 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 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -32 -1 12 13 8 3 4 17 48 103 188 309 472 683 948 1273 1664 2127 2668 3293 4008 4819 5732 6753 7888 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 0 -2 12 -114 1800 -42440 1386000 -59708810 3276129360 -222879971412 18403766756760 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 1 -3 13 -119 1881 -44379 1449477 -62444367 3426233521 -233091877523 19246991221437 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 -2 13 -74 243 13896 -898375 48043318 -2644884473 153403353676 -8950893339291 436954169955304 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A104684 | 1 2 1 6 6 1 20 30 12 1 70 140 90 20 1 252 630 560 210 30 1 924 2772 3150 1680 420 42 1 3432 12012 |
| Inv:Rev | Accsee docs | missing | 1 1 -1 1 -5 1 1 -11 31 -1 1 -19 131 -309 1 1 -29 361 -2179 4931 -1 1 -41 799 -8861 51829 -116423 1 |
| Inv:Rev | AccRevsee docs | missing | 1 -2 -1 6 0 1 -32 10 -2 -1 310 -130 20 0 1 -4932 2178 -362 28 -2 -1 116424 -51828 8862 -798 42 0 1 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -2 1 -6 1 -12 6 1 -20 42 1 -30 150 -32 1 -42 390 -440 1 -56 840 -2540 310 1 -72 1596 -9660 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -4 1 -12 18 1 -24 126 -128 1 -40 450 -1760 1550 1 -60 1170 -10160 35550 -29592 1 -84 2520 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 7 43 461 7501 177955 5817799 250675801 13754614921 935751981407 77267496160339 7610339286733925 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -2 -6 -44 -460 -7502 -177954 -5817800 -250675800 -13754614922 -935751981406 -77267496160340 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 3 13 87 921 15003 355909 11635599 501351601 27509229843 1871503962813 154534992320679 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | missing | 1 3 13 87 921 15003 355909 11635599 501351601 27509229843 1871503962813 154534992320679 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 -1 -5 -5 23 89 -91 -1445 -1025 29881 83477 -779819 -4619015 23820935 274709003 -727641013 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 0 -3 20 -195 3084 -72695 2373888 -102265695 5611148000 -381734646579 31520799931620 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -3 7 -25 201 -3091 72703 -2373897 102265705 -5611148011 381734646591 -31520799931633 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 2 6 672 204600 3216379140 7750311334920 131426737497966879360 54722432423401919925487384726080 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 2 6 2 10 2 42 2 6 2 22 2 26 2 2 2 34 2 114 2 30 2 46 2 30 2 6 2 58 2 62 2 2 2 2 2 74 2 2 2 82 2 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 2 6 42 440 7110 168252 5497632 236856384 12996105750 884146372340 73006244474196 7190633348844816 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -6 -12 150 390 -9660 -28560 1240470 3936870 -268199316 -889418376 87622410876 299376289212 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 -6 150 -9660 1240470 -268199316 87622410876 -40261266559800 24737671557915030 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -12 390 -28560 3936870 -889418376 299376289212 -140561186800320 87789560955898230 |
| 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 | ColRightT(n, n) | missing | 1 -2 6 -32 310 -4932 116424 -3802752 163825974 -8988907100 611529126076 -50495522176992 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 -1 -5 59 -629 8969 -163589 3149075 -21014069 -5852034211 899181599845 -115896134963995 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -3 19 -195 3051 -69933 2242339 -96184707 5316455755 -367541743353 31038259817709 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 -2 6 -24 200 -3090 72702 -2373896 102265704 -5611148010 381734646590 -31520799931632 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -3 7 -25 201 -3091 72703 -2373897 102265705 -5611148011 381734646591 -31520799931633 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -2 18 -132 1580 -30870 872382 -33234488 1636251192 -101000664090 7634692931690 -693457598495772 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 0 -2 12 -114 1800 -42440 1386000 -59708810 3276129360 -222879971412 18403766756760 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -4 22 -172 1966 -32944 787816 -25804048 1112263798 -61034491144 4152344656252 -342870809069848 |
| Inv:Rev | DiagRow1T(n + 1, n) | missing | 1 -6 42 -440 7110 -168252 5497632 -236856384 12996105750 -884146372340 73006244474196 |
| Inv:Rev | DiagRow2T(n + 2, n) | missing | 1 -12 150 -2540 60690 -1986432 85606584 -4697384400 319573375110 -26388034855160 2599047970783836 |
| Inv:Rev | DiagRow3T(n + 3, n) | missing | 1 -20 390 -9660 318570 -13748112 754567800 -51337094160 4239074011590 -417521481514280 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A002378 | -2 -6 -12 -20 -30 -42 -56 -72 -90 -110 -132 -156 -182 -210 -240 -272 -306 -342 -380 -420 -462 -506 |
| Inv:Rev | DiagCol2T(n + 2, 2) | missing | 6 42 150 390 840 1596 2772 4500 6930 10230 14586 20202 27300 36120 46920 59976 75582 94050 115710 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | -32 -440 -2540 -9660 -28560 -71232 -157080 -315480 -588720 -1035320 -1733732 -2786420 -4324320 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 -1 1 1 1 -3 1 1 -1 13 -5 1 1 1 -111 37 -7 1 1 -1 2001 -521 73 -9 1 1 1 -62883 14521 -1423 |
| Inv:Rev | PolyRow1∑ k=0..1 T(1, k) n^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 |
| Inv:Rev | PolyRow2∑ k=0..2 T(2, k) n^k | A003154 | 1 1 13 37 73 121 181 253 337 433 541 661 793 937 1093 1261 1441 1633 1837 2053 2281 2521 2773 3037 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 -1 -111 -521 -1423 -3009 -5471 -9001 -13791 -20033 -27919 -37641 -49391 -63361 -79743 -98729 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -3 13 -111 2001 -62883 2964109 -193594719 16680002593 -1830409796163 249050983487373 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -5 37 -521 14521 -687725 48650365 -4766500625 616022291665 -101400558093845 20695294322230837 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 -1 13 -521 53521 -11276649 4200148261 -2517569677489 2273815711683265 -2945117481084267857 |
| << | 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.