OEIS Similars: A056857, A056860
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A056857 | 1 1 1 2 2 1 5 6 3 1 15 20 12 4 1 52 75 50 20 5 1 203 312 225 100 30 6 1 877 1421 1092 525 175 42 7 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A056860 | 1 1 1 1 2 2 1 3 6 5 1 4 12 20 15 1 5 20 50 75 52 1 6 30 100 225 312 203 1 7 42 175 525 1092 1421 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A129334 | 1 -1 1 0 -2 1 1 0 -3 1 1 4 0 -4 1 -2 5 10 0 -5 1 -9 -12 15 20 0 -6 1 -9 -63 -42 35 35 0 -7 1 50 -72 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A143987 | 1 1 -1 1 -2 0 1 -3 0 1 1 -4 0 4 1 1 -5 0 10 5 -2 1 -6 0 20 15 -12 -9 1 -7 0 35 35 -42 -63 -9 1 -8 0 |
| Std | Accsee docs | missing | 1 1 2 2 4 5 5 11 14 15 15 35 47 51 52 52 127 177 197 202 203 203 515 740 840 870 876 877 877 2298 |
| Std | AccRevsee docs | missing | 1 1 2 1 3 5 1 4 10 15 1 5 17 37 52 1 6 26 76 151 203 1 7 37 137 362 674 877 1 8 50 225 750 1842 |
| Std | AntiDiagsee docs | missing | 1 1 2 1 5 2 15 6 1 52 20 3 203 75 12 1 877 312 50 4 4140 1421 225 20 1 21147 7016 1092 100 5 115975 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 2 4 3 5 12 9 4 15 40 36 16 5 52 150 150 80 25 6 203 624 675 400 150 36 7 877 2842 3276 2100 |
| Std | RowSum∑ k=0..n T(n, k) | A000110 | 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A224271 | 1 1 3 8 28 107 459 2151 10931 59700 348146 2155925 14112377 97266301 703484851 5323515156 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A102286 | 0 1 2 7 24 96 418 1989 10216 56275 330424 2057672 13532060 93633021 679473694 5156626991 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000296 | 1 0 1 1 4 11 41 162 715 3425 17722 98253 580317 3633280 24011157 166888165 1216070380 9264071767 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000110 | 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 3 7 22 75 291 1243 5807 29360 159475 924705 5693767 37062441 254058110 1827864405 13762384463 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 11 45 200 958 4921 26981 157203 969427 6304520 43098894 308814517 2313212827 18071787667 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A124427 | 1 3 9 30 112 463 2095 10279 54267 306298 1838320 11677867 78207601 550277003 4055549053 31224520322 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 30 60 3900 4750200 4860246300 2682855957600 1215736177186440 56398001259678951600 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 2 1 1 1 1 1 2 3 1 1 1 1 1 1 1 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 |
| Std | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 20 75 312 1421 7016 37260 211470 1275725 8142840 54776761 387022118 2902665885 22907918640 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 2 6 12 50 100 525 1050 6552 13104 93786 187572 1504932 3009864 26640900 53281800 514083570 |
| Std | CentralET(2 n, n) | A124102 | 1 2 12 100 1050 13104 187572 3009864 53281800 1028167140 21427077100 478684992240 11394223609132 |
| Std | CentralOT(2 n + 1, n) | A297926 | 1 6 50 525 6552 93786 1504932 26640900 514083570 10713538550 239342496120 5697111804566 |
| Std | ColLeftT(n, 0) | A000110 | 1 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| 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 7 33 184 1153 7937 59188 473305 4027093 36235134 343102037 3405004093 35297145406 381093334811 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -1 5 -8 -1 121 -778 3417 -10211 -482 324279 -3394467 25259324 -151291373 672971613 -805657164 |
| Std | TransNat0∑ k=0..n T(n, k) k | A070071 | 0 1 4 15 60 260 1218 6139 33120 190323 1159750 7464270 50563164 359377681 2672590508 20744378175 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A124427 | 1 3 9 30 112 463 2095 10279 54267 306298 1838320 11677867 78207601 550277003 4055549053 31224520322 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | A175716 | 0 1 6 27 120 560 2778 14665 82232 488403 3062980 20221520 140134404 1016698813 7703878042 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A126390 | 1 3 13 71 457 3355 27509 248127 2434129 25741939 291397789 3510328695 44782460313 602513988107 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A124311 | 1 -1 5 -21 121 -793 5917 -49101 447153 -4421105 47062773 -535732805 6484924585 -83079996041 |
| Std | DiagRow1T(n + 1, n) | 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 | DiagRow2T(n + 2, 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 | DiagRow3T(n + 3, n) | A134481 | 5 20 50 100 175 280 420 600 825 1100 1430 1820 2275 2800 3400 4080 4845 5700 6650 7700 8855 10120 |
| Std | DiagCol1T(n + 1, 1) | A052889 | 1 2 6 20 75 312 1421 7016 37260 211470 1275725 8142840 54776761 387022118 2863489830 22127336720 |
| Std | DiagCol2T(n + 2, 2) | A105479 | 1 3 12 50 225 1092 5684 31572 186300 1163085 7654350 52928460 383437327 2902665885 22907918640 |
| Std | DiagCol3T(n + 3, 3) | A105480 | 1 4 20 100 525 2912 17052 105240 683100 4652340 33168850 246999480 1917186635 15480884720 |
| Std | Polysee docs | A108087 | 1 1 1 2 2 1 5 5 3 1 15 15 10 4 1 52 52 37 17 5 1 203 203 151 77 26 6 1 877 877 674 372 141 37 7 1 |
| 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 | A002522 | 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 730 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A005491 | 5 15 37 77 141 235 365 537 757 1031 1365 1765 2237 2787 3421 4145 4965 5887 6917 8061 9325 10715 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A005493 | 1 3 10 37 151 674 3263 17007 94828 562595 3535027 23430840 163254885 1192059223 9097183602 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A005494 | 1 4 17 77 372 1915 10481 60814 372939 2409837 16360786 116393205 865549453 6713065156 54190360453 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A134980 | 1 2 10 77 799 10427 163967 3017562 63625324 1512354975 40012800675 1166271373797 37134022033885 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A056857 | 1 1 -1 2 -2 1 5 -6 3 -1 15 -20 12 -4 1 52 -75 50 -20 5 -1 203 -312 225 -100 30 -6 1 877 -1421 1092 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A056860 | 1 -1 1 1 -2 2 -1 3 -6 5 1 -4 12 -20 15 -1 5 -20 50 -75 52 1 -6 30 -100 225 -312 203 -1 7 -42 175 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -4 2 1 1 0 -3 1 17 -4 -24 4 1 8 -5 10 0 -5 1 23 -48 255 -20 -60 6 1 -205 63 168 -35 35 0 -7 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 2 -4 1 -3 0 1 1 4 -24 -4 17 1 -5 0 10 -5 8 1 6 -60 -20 255 -48 23 1 -7 0 35 -35 168 63 |
| Alt | Accsee docs | missing | 1 1 0 2 0 1 5 -1 2 1 15 -5 7 3 4 52 -23 27 7 12 11 203 -109 116 16 46 40 41 877 -544 548 23 198 156 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -1 1 -1 2 -4 1 1 -3 9 -11 4 -1 4 -16 34 -41 11 1 -5 25 -75 150 -162 41 -1 6 -36 139 -386 |
| Alt | AntiDiagsee docs | missing | 1 1 2 -1 5 -2 15 -6 1 52 -20 3 203 -75 12 -1 877 -312 50 -4 4140 -1421 225 -20 1 21147 -7016 1092 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 2 -4 3 5 -12 9 -4 15 -40 36 -16 5 52 -150 150 -80 25 -6 203 -624 675 -400 150 -36 7 877 |
| Alt | RowSum∑ k=0..n T(n, k) | A000296 | 1 0 1 1 4 11 41 162 715 3425 17722 98253 580317 3633280 24011157 166888165 1216070380 9264071767 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A224271 | 1 1 3 8 28 107 459 2151 10931 59700 348146 2155925 14112377 97266301 703484851 5323515156 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A102286 | 0 -1 -2 -7 -24 -96 -418 -1989 -10216 -56275 -330424 -2057672 -13532060 -93633021 -679473694 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000110 | 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000110 | 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A184175 | 1 1 1 3 10 35 139 611 2925 15128 83903 495929 3108129 20565721 143134606 1044489265 7968879387 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 3 7 24 86 353 1583 7731 40685 229192 1373978 8723157 58410041 411033275 3030377995 23343407100 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 1 -2 0 -9 -25 -125 -581 -3010 -16528 -96689 -598719 -3910841 -26854763 -193279190 -1454140260 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 30 60 3900 4750200 4860246300 2682855957600 1215736177186440 56398001259678951600 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 2 1 1 1 1 1 2 3 1 1 1 1 1 1 1 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 |
| Alt | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 20 75 312 1421 7016 37260 211470 1275725 8142840 54776761 387022118 2902665885 22907918640 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -2 -6 12 50 -100 -525 1050 6552 -13104 -93786 187572 1504932 -3009864 -26640900 53281800 |
| Alt | CentralET(2 n, n) | A124102 | 1 -2 12 -100 1050 -13104 187572 -3009864 53281800 -1028167140 21427077100 -478684992240 |
| Alt | CentralOT(2 n + 1, n) | A297926 | 1 -6 50 -525 6552 -93786 1504932 -26640900 514083570 -10713538550 239342496120 -5697111804566 |
| Alt | ColLeftT(n, 0) | A000110 | 1 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -1 -5 -8 1 121 778 3417 10211 -482 -324279 -3394467 -25259324 -151291373 -672971613 -805657164 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 7 -33 184 -1153 7937 -59188 473305 -4027093 36235134 -343102037 3405004093 -35297145406 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A250105 | 0 -1 0 -3 -4 -20 -66 -287 -1296 -6435 -34250 -194942 -1179036 -7544121 -50865920 -360167355 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 1 -2 0 -9 -25 -125 -581 -3010 -16528 -96689 -598719 -3910841 -26854763 -193279190 -1454140260 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 2 -3 8 0 54 175 1000 5229 30100 181808 1160268 7783347 54751774 402821445 3092467040 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A124311 | 1 1 5 21 121 793 5917 49101 447153 4421105 47062773 535732805 6484924585 83079996041 1121947980173 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A126390 | 1 -3 13 -71 457 -3355 27509 -248127 2434129 -25741939 291397789 -3510328695 44782460313 |
| Alt | DiagRow1T(n + 1, n) | 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 |
| Alt | DiagRow2T(n + 2, 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 | DiagRow3T(n + 3, n) | A134481 | 5 -20 50 -100 175 -280 420 -600 825 -1100 1430 -1820 2275 -2800 3400 -4080 4845 -5700 6650 -7700 |
| Alt | DiagCol1T(n + 1, 1) | A052889 | -1 -2 -6 -20 -75 -312 -1421 -7016 -37260 -211470 -1275725 -8142840 -54776761 -387022118 -2863489830 |
| Alt | DiagCol2T(n + 2, 2) | A105479 | 1 3 12 50 225 1092 5684 31572 186300 1163085 7654350 52928460 383437327 2902665885 22907918640 |
| Alt | DiagCol3T(n + 3, 3) | A105480 | -1 -4 -20 -100 -525 -2912 -17052 -105240 -683100 -4652340 -33168850 -246999480 -1917186635 |
| Alt | Polysee docs | missing | 1 1 1 2 0 1 5 1 -1 1 15 1 2 -2 1 52 4 -3 5 -3 1 203 11 7 -13 10 -4 1 877 41 -10 36 -35 17 -5 1 4140 |
| 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 | A002522 | 2 1 2 5 10 17 26 37 50 65 82 101 122 145 170 197 226 257 290 325 362 401 442 485 530 577 626 677 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 5 1 -3 -13 -35 -75 -139 -233 -363 -535 -755 -1029 -1363 -1763 -2235 -2785 -3419 -4143 -4963 -5885 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A126617 | 1 -1 2 -3 7 -10 31 -21 204 307 2811 12100 74053 432211 2768858 18473441 129941283 956187814 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A346738 | 1 -2 5 -13 36 -101 293 -848 2523 -7365 22402 -64395 205285 -541802 2057617 -3403993 28685420 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A290219 | 1 0 2 -13 127 -1573 23711 -421356 8626668 -199971255 5177291275 -148078588667 4636966634653 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A056860 | 1 1 1 1 2 2 1 3 6 5 1 4 12 20 15 1 5 20 50 75 52 1 6 30 100 225 312 203 1 7 42 175 525 1092 1421 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A129334 | 1 -1 1 0 -2 1 1 0 -3 1 1 4 0 -4 1 -2 5 10 0 -5 1 -9 -12 15 20 0 -6 1 -9 -63 -42 35 35 0 -7 1 50 -72 |
| Rev | Accsee docs | missing | 1 1 2 1 3 5 1 4 10 15 1 5 17 37 52 1 6 26 76 151 203 1 7 37 137 362 674 877 1 8 50 225 750 1842 |
| Rev | AccRevsee docs | missing | 1 1 2 2 4 5 5 11 14 15 15 35 47 51 52 52 127 177 197 202 203 203 515 740 840 870 876 877 877 2298 |
| Rev | AntiDiagsee docs | missing | 1 1 1 1 1 2 1 3 2 1 4 6 1 5 12 5 1 6 20 20 1 7 30 50 15 1 8 42 100 75 1 9 56 175 225 52 1 10 72 280 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 4 6 1 6 18 20 1 8 36 80 75 1 10 60 200 375 312 1 12 90 400 1125 1872 1421 1 14 126 700 2625 |
| Rev | RowSum∑ k=0..n T(n, k) | A000110 | 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 3 7 28 96 459 1989 10931 56275 348146 2057672 14112377 93633021 703484851 5156626991 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 2 8 24 107 418 2151 10216 59700 330424 2155925 13532060 97266301 679473694 5323515156 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A000296 | 1 0 1 -1 4 -11 41 -162 715 -3425 17722 -98253 580317 -3633280 24011157 -166888165 1216070380 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000110 | 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A303586 | 1 1 2 3 6 11 23 47 103 226 518 1200 2867 6946 17234 43393 111419 290242 768901 2065172 5630083 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A124427 | 1 3 9 30 112 463 2095 10279 54267 306298 1838320 11677867 78207601 550277003 4055549053 31224520322 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 11 45 200 958 4921 26981 157203 969427 6304520 43098894 308814517 2313212827 18071787667 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 30 60 3900 4750200 4860246300 2682855957600 1215736177186440 56398001259678951600 |
| Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 2 1 1 1 1 1 2 3 1 1 1 1 1 1 1 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 |
| Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 6 20 75 312 1421 7016 37260 211470 1275725 8142840 54776761 387022118 2902665885 22907918640 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 2 3 12 20 100 175 1050 1890 13104 24024 187572 348348 3009864 5643495 53281800 100643400 |
| Rev | CentralET(2 n, n) | A124102 | 1 2 12 100 1050 13104 187572 3009864 53281800 1028167140 21427077100 478684992240 11394223609132 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 3 20 175 1890 24024 348348 5643495 100643400 1953517566 40906238100 917479568460 21911968479100 |
| 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) | A000110 | 1 1 2 5 15 52 203 877 4140 21147 115975 678570 4213597 27644437 190899322 1382958545 10480142147 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 7 33 184 1153 7937 59188 473305 4027093 36235134 343102037 3405004093 35297145406 381093334811 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -1 -5 -8 1 121 778 3417 10211 -482 -324279 -3394467 -25259324 -151291373 -672971613 -805657164 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A127741 | 0 1 6 30 148 755 4044 22841 136056 853452 5625950 38885297 281170080 2122313505 16688829122 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 11 45 200 958 4921 26981 157203 969427 6304520 43098894 308814517 2313212827 18071787667 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 10 72 472 3035 19734 131579 905720 6456564 47724980 365852817 2907417396 23934864525 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A005493 | 1 3 10 37 151 674 3263 17007 94828 562595 3535027 23430840 163254885 1192059223 9097183602 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A126617 | 1 -1 2 -3 7 -10 31 -21 204 307 2811 12100 74053 432211 2768858 18473441 129941283 956187814 |
| Rev | DiagRow1T(n + 1, n) | A052889 | 1 2 6 20 75 312 1421 7016 37260 211470 1275725 8142840 54776761 387022118 2863489830 22127336720 |
| Rev | DiagRow2T(n + 2, n) | A105479 | 1 3 12 50 225 1092 5684 31572 186300 1163085 7654350 52928460 383437327 2902665885 22907918640 |
| Rev | DiagRow3T(n + 3, n) | A105480 | 1 4 20 100 525 2912 17052 105240 683100 4652340 33168850 246999480 1917186635 15480884720 |
| Rev | DiagCol1T(n + 1, 1) | 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 | DiagCol2T(n + 2, 2) | 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 | DiagCol3T(n + 3, 3) | A134481 | 5 20 50 100 175 280 420 600 825 1100 1430 1820 2275 2800 3400 4080 4845 5700 6650 7700 8855 10120 |
| Rev | Polysee docs | missing | 1 1 1 1 2 1 1 5 3 1 1 15 13 4 1 1 52 71 25 5 1 1 203 457 199 41 6 1 1 877 3355 1876 429 61 7 1 1 |
| 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 | A001844 | 1 5 13 25 41 61 85 113 145 181 221 265 313 365 421 481 545 613 685 761 841 925 1013 1105 1201 1301 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 15 71 199 429 791 1315 2031 2969 4159 5631 7415 9541 12039 14939 18271 22065 26351 31159 36519 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A126390 | 1 3 13 71 457 3355 27509 248127 2434129 25741939 291397789 3510328695 44782460313 602513988107 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A284859 | 1 4 25 199 1876 20257 245017 3266914 47450923 743935375 12497579698 223619318215 4240423494685 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A307066 | 1 2 13 199 5329 216151 12211597 909102342 85761187393 9957171535975 1390946372509101 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A129334 | 1 -1 1 0 -2 1 1 0 -3 1 1 4 0 -4 1 -2 5 10 0 -5 1 -9 -12 15 20 0 -6 1 -9 -63 -42 35 35 0 -7 1 50 -72 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A143987 | 1 1 -1 1 -2 0 1 -3 0 1 1 -4 0 4 1 1 -5 0 10 5 -2 1 -6 0 20 15 -12 -9 1 -7 0 35 35 -42 -63 -9 1 -8 0 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A056860 | 1 1 1 1 2 2 1 3 6 5 1 4 12 20 15 1 5 20 50 75 52 1 6 30 100 225 312 203 1 7 42 175 525 1092 1421 |
| Inv | Accsee docs | missing | 1 -1 0 0 -2 -1 1 1 -2 -1 1 5 5 1 2 -2 3 13 13 8 9 -9 -21 -6 14 14 8 9 -9 -72 -114 -79 -44 -44 -51 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -1 -1 1 -2 -2 -1 1 -3 -3 1 2 1 -4 -4 6 11 9 1 -5 -5 15 30 18 9 1 -6 -6 29 64 22 -41 -50 1 |
| Inv | AntiDiagsee docs | missing | 1 -1 0 1 1 -2 1 0 1 -2 4 -3 -9 5 0 1 -9 -12 10 -4 50 -63 15 0 1 267 -72 -42 20 -5 413 450 -252 35 0 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 0 -4 3 1 0 -9 4 1 8 0 -16 5 -2 10 30 0 -25 6 -9 -24 45 80 0 -36 7 -9 -126 -126 140 175 0 -49 |
| Inv | RowSum∑ k=0..n T(n, k) | A000587 | 1 0 -1 -1 2 9 9 -50 -267 -413 2180 17731 50533 -110176 -1966797 -9938669 -8638718 278475061 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 1 -2 2 3 7 -23 -131 -234 984 8765 26457 -47413 -965807 -5042014 -5230078 135178915 1270217511 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -2 1 0 6 2 -27 -136 -179 1196 8966 24076 -62763 -1000990 -4896655 -3408640 143296146 1270738998 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A109747 | 1 -2 3 -3 2 -3 5 4 5 -55 -212 -201 2381 15350 35183 -145359 -1821438 -8117231 -521487 278996548 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 3 5 10 23 63 192 621 2269 9148 38217 172395 858926 4386075 22977833 131911130 793007975 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 1 -1 2 -1 -3 -15 3 168 647 83 -11623 -63291 -86582 1144637 10116709 34190949 -103894395 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -3 -1 14 44 9 -463 -2003 -1727 28110 188792 444157 -2199393 -27959491 -129516749 12160498 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -1 -4 -2 19 63 13 -667 -2816 -1950 41711 263305 546753 -3509261 -39440624 -167657422 131616855 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 4 10 180 630 25200 5046300 992439000 594967180500 18084622418478000 56572918670230162200 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 4 1 1 1 2 3 1 1 1 1 1 1 1 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 2 3 4 10 20 63 252 756 2670 14685 58740 230503 1613521 8067605 32270420 267484392 1604906352 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -2 0 0 10 20 35 70 -252 -504 -4158 -8316 -15444 -30888 321750 643500 6490770 12981540 38152114 |
| Inv | CentralET(2 n, n) | missing | 1 -2 0 20 70 -504 -8316 -30888 643500 12981540 76304228 -1537841760 -47947390036 -525573519800 |
| Inv | CentralOT(2 n + 1, n) | missing | -1 0 10 35 -252 -4158 -15444 321750 6490770 38152114 -768920880 -23973695018 -262786759900 |
| Inv | ColLeftT(n, 0) | A000587 | 1 -1 0 1 1 -2 -9 -9 50 267 413 -2180 -17731 -50533 110176 1966797 9938669 8638718 -278475061 |
| 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 -3 -7 2 99 509 1070 -5881 -79751 -466744 -975261 12350821 181063388 1295346545 3606195697 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 5 9 2 -47 -75 500 1671 -7403 -35528 173517 836357 -5837426 -19653447 244486889 266453718 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 0 -3 -4 10 54 63 -400 -2403 -4130 23980 212772 656929 -1542464 -29501955 -159018704 -146858206 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -1 -4 -2 19 63 13 -667 -2816 -1950 41711 263305 546753 -3509261 -39440624 -167657422 131616855 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 2 -3 -16 -10 114 441 104 -6003 -28160 -21450 500532 3422965 7654542 -52638915 -631049984 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A308645 | 1 -1 -3 3 41 87 -571 -5701 -14575 156655 2094925 9148851 -63364423 -1474212665 -11494853995 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A367743 | 1 3 5 -1 -7 75 -99 -1241 10161 -18989 -332299 3857551 -14440151 -141168997 2807256333 -20182451657 |
| Inv | DiagRow1T(n + 1, n) | 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 |
| Inv | DiagRow3T(n + 3, n) | A000292 | 1 4 10 20 35 56 84 120 165 220 286 364 455 560 680 816 969 1140 1330 1540 1771 2024 2300 2600 2925 |
| Inv | DiagCol1T(n + 1, 1) | missing | 1 -2 0 4 5 -12 -63 -72 450 2670 4543 -26160 -230503 -707462 1652640 31468752 168957373 155496924 |
| Inv | DiagCol2T(n + 2, 2) | missing | 1 -3 0 10 15 -42 -252 -324 2250 14685 27258 -170040 -1613521 -5305965 13221120 267484392 1520616357 |
| Inv | DiagCol3T(n + 3, 3) | missing | 1 -4 0 20 35 -112 -756 -1080 8250 58740 118118 -793520 -8067605 -28298480 74919680 1604906352 |
| Inv | Polysee docs | missing | 1 -1 1 0 0 1 1 -1 1 1 1 -1 0 2 1 -2 2 -3 3 3 1 -9 9 -7 1 8 4 1 -9 9 0 -14 17 15 5 1 50 -50 59 -59 |
| 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 | A005563 | 0 -1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 -1 -3 1 17 51 109 197 321 487 701 969 1297 1691 2157 2701 3329 4047 4861 5777 6801 7939 9197 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A074051 | 1 1 0 -3 -7 0 59 217 146 -2593 -15551 -32802 160709 1856621 7971872 -1299951 -287113779 -2262481448 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | A193683 | 1 2 3 1 -14 -59 -99 288 2885 10365 1700 -226313 -1535203 -4258630 17243695 284513877 1688253890 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | A298373 | 1 0 0 1 17 273 4779 93532 2047730 49854795 1339872113 39462731031 1265248227869 43895994373580 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A143987 | 1 1 -1 1 -2 0 1 -3 0 1 1 -4 0 4 1 1 -5 0 10 5 -2 1 -6 0 20 15 -12 -9 1 -7 0 35 35 -42 -63 -9 1 -8 0 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A129334 | 1 -1 1 0 -2 1 1 0 -3 1 1 4 0 -4 1 -2 5 10 0 -5 1 -9 -12 15 20 0 -6 1 -9 -63 -42 35 35 0 -7 1 50 -72 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A056857 | 1 1 1 2 2 1 5 6 3 1 15 20 12 4 1 52 75 50 20 5 1 203 312 225 100 30 6 1 877 1421 1092 525 175 42 7 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -1 -1 1 -2 -2 -1 1 -3 -3 1 2 1 -4 -4 6 11 9 1 -5 -5 15 30 18 9 1 -6 -6 29 64 22 -41 -50 1 |
| Inv:Rev | AccRevsee docs | missing | 1 -1 0 0 -2 -1 1 1 -2 -1 1 5 5 1 2 -2 3 13 13 8 9 -9 -21 -6 14 14 8 9 -9 -72 -114 -79 -44 -44 -51 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -2 1 -3 0 1 -4 0 1 -5 0 1 1 -6 0 4 1 -7 0 10 1 1 -8 0 20 5 1 -9 0 35 15 -2 1 -10 0 56 35 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -4 0 1 -6 0 4 1 -8 0 16 5 1 -10 0 40 25 -12 1 -12 0 80 75 -72 -63 1 -14 0 140 175 -252 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A000587 | 1 0 -1 -1 2 9 9 -50 -267 -413 2180 17731 50533 -110176 -1966797 -9938669 -8638718 278475061 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 1 1 2 6 7 -27 -131 -179 984 8966 26457 -62763 -965807 -4896655 -5230078 143296146 1270217511 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -2 -2 0 3 2 -23 -136 -234 1196 8765 24076 -47413 -1000990 -5042014 -3408640 135178915 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A109747 | 1 2 3 3 2 3 5 -4 5 55 -212 201 2381 -15350 35183 145359 -1821438 8117231 -521487 -278996548 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 3 5 10 23 63 192 621 2269 9148 38217 172395 858926 4386075 22977833 131911130 793007975 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -1 -2 -3 -3 -1 5 18 40 70 93 60 -150 -795 -2321 -5308 -9903 -13748 -6147 46141 227779 721757 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -1 -4 -2 19 63 13 -667 -2816 -1950 41711 263305 546753 -3509261 -39440624 -167657422 131616855 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -3 -1 14 44 9 -463 -2003 -1727 28110 188792 444157 -2199393 -27959491 -129516749 12160498 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 4 10 180 630 25200 5046300 992439000 594967180500 18084622418478000 56572918670230162200 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 4 1 1 1 2 3 1 1 1 1 1 1 1 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 2 3 4 10 20 63 252 756 2670 14685 58740 230503 1613521 8067605 32270420 267484392 1604906352 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -2 -3 0 0 20 35 70 126 -504 -924 -8316 -15444 -30888 -57915 643500 1215500 12981540 24664926 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 -2 0 20 70 -504 -8316 -30888 643500 12981540 76304228 -1537841760 -47947390036 -525573519800 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -3 0 35 126 -924 -15444 -57915 1215500 24664926 145671708 -2947530040 -92206519300 -1013606073900 |
| 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) | A000587 | 1 -1 0 1 1 -2 -9 -9 50 267 413 -2180 -17731 -50533 110176 1966797 9938669 8638718 -278475061 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -3 -7 2 99 509 1070 -5881 -79751 -466744 -975261 12350821 181063388 1295346545 3606195697 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 5 -9 2 47 -75 -500 1671 7403 -35528 -173517 836357 5837426 -19653447 -244486889 266453718 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 -2 0 12 35 0 -413 -1736 -1314 25930 171061 393624 -2089217 -25992694 -119578080 20799216 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -3 -1 14 44 9 -463 -2003 -1727 28110 188792 444157 -2199393 -27959491 -129516749 12160498 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 -2 6 48 115 -210 -2891 -10584 3798 272440 1596441 2670756 -32276933 -334648678 -1403780790 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A074051 | 1 1 0 -3 -7 0 59 217 146 -2593 -15551 -32802 160709 1856621 7971872 -1299951 -287113779 -2262481448 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A153732 | 1 -3 8 -19 41 -84 171 -347 690 -1385 2825 -5438 11077 -24535 33720 -102623 350605 1120228 5876775 |
| Inv:Rev | DiagRow1T(n + 1, n) | missing | 1 -2 0 4 5 -12 -63 -72 450 2670 4543 -26160 -230503 -707462 1652640 31468752 168957373 155496924 |
| Inv:Rev | DiagRow2T(n + 2, n) | missing | 1 -3 0 10 15 -42 -252 -324 2250 14685 27258 -170040 -1613521 -5305965 13221120 267484392 1520616357 |
| Inv:Rev | DiagRow3T(n + 3, n) | missing | 1 -4 0 20 35 -112 -756 -1080 8250 58740 118118 -793520 -8067605 -28298480 74919680 1604906352 |
| Inv:Rev | DiagCol1T(n + 1, 1) | 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 |
| Inv:Rev | DiagCol3T(n + 3, 3) | A000292 | 1 4 10 20 35 56 84 120 165 220 286 364 455 560 680 816 969 1140 1330 1540 1771 2024 2300 2600 2925 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 -1 -1 1 1 -1 -3 -2 1 1 2 3 -5 -3 1 1 9 41 19 -7 -4 1 1 9 87 178 53 -9 -5 1 1 -50 -571 |
| 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 | 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 | PolyRow3∑ k=0..3 T(3, k) n^k | A177058 | 1 -1 3 19 53 111 199 323 489 703 971 1299 1693 2159 2703 3331 4049 4863 5779 6803 7941 9199 10583 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A308645 | 1 -1 -3 3 41 87 -571 -5701 -14575 156655 2094925 9148851 -63364423 -1474212665 -11494853995 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A284860 | 1 -2 -5 19 178 175 -7739 -72056 -33179 6899311 87861076 215532301 -11151014291 -222077806202 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | A307080 | 1 0 -3 19 497 -1899 -489491 -15433676 618450881 120846851155 7012261819901 -467816186167659 |
| << | 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.