OEIS Similars: A059481, A027555
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A059481 | 1 1 1 1 2 3 1 3 6 10 1 4 10 20 35 1 5 15 35 70 126 1 6 21 56 126 252 462 1 7 28 84 210 462 924 1716 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A100100 | 1 1 1 3 2 1 10 6 3 1 35 20 10 4 1 126 70 35 15 5 1 462 252 126 56 21 6 1 1716 924 462 210 84 28 7 1 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A100218 | 1 -1 1 -1 -2 1 -1 0 -3 1 -1 0 2 -4 1 -1 0 0 5 -5 1 -1 0 0 -2 9 -6 1 -1 0 0 0 -7 14 -7 1 -1 0 0 0 2 |
| Std | Accsee docs | A046899 | 1 1 2 1 3 6 1 4 10 20 1 5 15 35 70 1 6 21 56 126 252 1 7 28 84 210 462 924 1 8 36 120 330 792 1716 |
| Std | AccRevsee docs | missing | 1 1 2 3 5 6 10 16 19 20 35 55 65 69 70 126 196 231 246 251 252 462 714 840 896 917 923 924 1716 |
| Std | AntiDiagsee docs | missing | 1 1 1 1 1 2 1 3 3 1 4 6 1 5 10 10 1 6 15 20 1 7 21 35 35 1 8 28 56 70 1 9 36 84 126 126 1 10 45 120 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 4 9 1 6 18 40 1 8 30 80 175 1 10 45 140 350 756 1 12 63 224 630 1512 3234 1 14 84 336 1050 |
| Std | RowSum∑ k=0..n T(n, k) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 4 7 46 86 610 1163 8518 16414 122464 237590 1794196 3497248 26635774 52097267 399300166 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 2 13 24 166 314 2269 4352 32206 62292 467842 909960 6903352 13480826 103020253 201780224 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A072547 | 1 0 2 -6 22 -80 296 -1106 4166 -15792 60172 -230252 884236 -3406104 13154948 -50922986 197519942 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A116406 | 1 1 2 3 7 11 26 42 99 163 382 638 1486 2510 5812 9908 22819 39203 89846 155382 354522 616666 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A001700 | 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A034275 | 1 3 14 65 294 1302 5676 24453 104390 442442 1864356 7818538 32657884 135950700 564306840 2336457645 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 30 140 630 5544 60060 51480 1531530 25865840 23279256 486748080 2230928700 6177956400 |
| 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) | | A001700 | 1 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Std | ColMiddleT(n, n // 2) | A081204 | 1 1 2 3 10 15 56 84 330 495 2002 3003 12376 18564 77520 116280 490314 735471 3124550 4686825 |
| Std | CentralET(2 n, n) | A165817 | 1 2 10 56 330 2002 12376 77520 490314 3124550 20030010 129024480 834451800 5414950296 35240152720 |
| Std | CentralOT(2 n + 1, n) | A005809 | 1 3 15 84 495 3003 18564 116280 735471 4686825 30045015 193536720 1251677700 8122425444 52860229080 |
| Std | 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 |
| Std | ColRightT(n, n) | A001700 | 1 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | A002003 | 1 2 8 38 192 1002 5336 28814 157184 864146 4780008 26572086 148321344 830764794 4666890936 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, 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 | TransNat0∑ k=0..n T(n, k) k | A110609 | 0 1 8 45 224 1050 4752 21021 91520 393822 1679600 7113106 29953728 125550100 524190240 2181340125 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A034275 | 1 3 14 65 294 1302 5676 24453 104390 442442 1864356 7818538 32657884 135950700 564306840 2336457645 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 14 117 784 4650 25542 133133 668096 3257982 15536300 72772546 335909664 1531711220 6912758790 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A032443 | 1 3 11 42 163 638 2510 9908 39203 155382 616666 2449868 9740686 38754732 154276028 614429672 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A367548 | 1 -1 3 2 19 54 222 804 3075 11630 44458 170268 654766 2524508 9758556 37802952 146724579 570450078 |
| Std | DiagRow1T(n + 1, n) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Std | DiagRow2T(n + 2, n) | A001700 | 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Std | DiagRow3T(n + 3, n) | A001791 | 1 4 15 56 210 792 3003 11440 43758 167960 646646 2496144 9657700 37442160 145422675 565722720 |
| Std | 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 |
| Std | DiagCol2T(n + 2, 2) | A000217 | 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Std | DiagCol3T(n + 3, 3) | A000292 | 10 20 35 56 84 120 165 220 286 364 455 560 680 816 969 1140 1330 1540 1771 2024 2300 2600 2925 3276 |
| Std | Polysee docs | missing | 1 1 1 1 2 1 1 6 3 1 1 20 17 4 1 1 70 111 34 5 1 1 252 769 334 57 6 1 1 924 5503 3478 749 86 7 1 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 | A056109 | 1 6 17 34 57 86 121 162 209 262 321 386 457 534 617 706 801 902 1009 1122 1241 1366 1497 1634 1777 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 20 111 334 749 1416 2395 3746 5529 7804 10631 14070 18181 23024 28659 35146 42545 50916 60319 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A119259 | 1 3 17 111 769 5503 40193 297727 2228225 16807935 127574017 973168639 7454392321 57298911231 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 34 334 3478 37384 409960 4558306 51199558 579554056 6600532684 75546800476 868224027916 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A368488 | 1 2 17 334 10417 442276 23690809 1530206742 115636017473 10004657077468 974950612575601 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A059481 | 1 1 -1 1 -2 3 1 -3 6 -10 1 -4 10 -20 35 1 -5 15 -35 70 -126 1 -6 21 -56 126 -252 462 1 -7 28 -84 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A100100 | 1 -1 1 3 -2 1 -10 6 -3 1 35 -20 10 -4 1 -126 70 -35 15 -5 1 462 -252 126 -56 21 -6 1 -1716 924 -462 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A100218 | 1 1 1 -1 2 1 1 0 3 1 -1 0 2 4 1 1 0 0 5 5 1 -1 0 0 2 9 6 1 1 0 0 0 7 14 7 1 -1 0 0 0 2 16 20 8 1 1 |
| Alt | Accsee docs | A201635 | 1 1 0 1 -1 2 1 -2 4 -6 1 -3 7 -13 22 1 -4 11 -24 46 -80 1 -5 16 -40 86 -166 296 1 -6 22 -62 148 |
| Alt | AccRevsee docs | missing | 1 -1 0 3 1 2 -10 -4 -7 -6 35 15 25 21 22 -126 -56 -91 -76 -81 -80 462 210 336 280 301 295 296 -1716 |
| Alt | AntiDiagsee docs | missing | 1 1 1 -1 1 -2 1 -3 3 1 -4 6 1 -5 10 -10 1 -6 15 -20 1 -7 21 -35 35 1 -8 28 -56 70 1 -9 36 -84 126 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -4 9 1 -6 18 -40 1 -8 30 -80 175 1 -10 45 -140 350 -756 1 -12 63 -224 630 -1512 3234 1 -14 |
| Alt | RowSum∑ k=0..n T(n, k) | A072547 | 1 0 2 -6 22 -80 296 -1106 4166 -15792 60172 -230252 884236 -3406104 13154948 -50922986 197519942 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 4 7 46 86 610 1163 8518 16414 122464 237590 1794196 3497248 26635774 52097267 399300166 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -2 -13 -24 -166 -314 -2269 -4352 -32206 -62292 -467842 -909960 -6903352 -13480826 -103020253 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A037952 | 1 1 0 -1 1 3 -4 -10 15 35 -56 -126 210 462 -792 -1716 3003 6435 -11440 -24310 43758 92378 -167960 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 2 -3 14 -50 188 -707 2678 -10194 38972 -149534 575548 -2221232 8592656 -33308771 129355430 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 6 -27 118 -510 2180 -9247 38982 -163518 683092 -2843742 11803756 -48870328 201886512 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 30 140 630 5544 60060 51480 1531530 25865840 23279256 486748080 2230928700 6177956400 |
| 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) | | A001700 | 1 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Alt | ColMiddleT(n, n // 2) | A081204 | 1 1 -2 -3 10 15 -56 -84 330 495 -2002 -3003 12376 18564 -77520 -116280 490314 735471 -3124550 |
| Alt | CentralET(2 n, n) | A165817 | 1 -2 10 -56 330 -2002 12376 -77520 490314 -3124550 20030010 -129024480 834451800 -5414950296 |
| Alt | CentralOT(2 n + 1, n) | A005809 | 1 -3 15 -84 495 -3003 18564 -116280 735471 -4686825 30045015 -193536720 1251677700 -8122425444 |
| Alt | 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 |
| Alt | ColRightT(n, n) | A001700 | 1 -1 3 -10 35 -126 462 -1716 6435 -24310 92378 -352716 1352078 -5200300 20058300 -77558760 |
| Alt | BinConv∑ k=0..n C(n, k) 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 | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A002003 | 1 -2 8 -38 192 -1002 5336 -28814 157184 -864146 4780008 -26572086 148321344 -830764794 4666890936 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 4 -21 96 -430 1884 -8141 34816 -147726 622920 -2613490 10919520 -45464224 188731564 -781459005 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 6 -27 118 -510 2180 -9247 38982 -163518 683092 -2843742 11803756 -48870328 201886512 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 10 -69 416 -2290 11922 -59661 289984 -1378206 6434660 -29611186 134641872 -606065356 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A367548 | 1 1 3 -2 19 -54 222 -804 3075 -11630 44458 -170268 654766 -2524508 9758556 -37802952 146724579 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A032443 | 1 -3 11 -42 163 -638 2510 -9908 39203 -155382 616666 -2449868 9740686 -38754732 154276028 |
| Alt | DiagRow1T(n + 1, n) | A000984 | 1 -2 6 -20 70 -252 924 -3432 12870 -48620 184756 -705432 2704156 -10400600 40116600 -155117520 |
| Alt | DiagRow2T(n + 2, n) | A001700 | 1 -3 10 -35 126 -462 1716 -6435 24310 -92378 352716 -1352078 5200300 -20058300 77558760 -300540195 |
| Alt | DiagRow3T(n + 3, n) | A001791 | 1 -4 15 -56 210 -792 3003 -11440 43758 -167960 646646 -2496144 9657700 -37442160 145422675 |
| Alt | 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 |
| Alt | DiagCol2T(n + 2, 2) | A000217 | 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Alt | DiagCol3T(n + 3, 3) | A000292 | -10 -20 -35 -56 -84 -120 -165 -220 -286 -364 -455 -560 -680 -816 -969 -1140 -1330 -1540 -1771 -2024 |
| Alt | Polysee docs | missing | 1 1 1 1 0 1 1 2 -1 1 1 -6 9 -2 1 1 22 -61 22 -3 1 1 -80 433 -224 41 -4 1 1 296 -3141 2374 -555 66 |
| 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 | A056105 | 1 2 9 22 41 66 97 134 177 226 281 342 409 482 561 646 737 834 937 1046 1161 1282 1409 1542 1681 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 -6 -61 -224 -555 -1114 -1961 -3156 -4759 -6830 -9429 -12616 -16451 -20994 -26305 -32444 -39471 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -1 9 -61 433 -3141 23145 -172509 1296993 -9817909 74726809 -571326669 4384519441 -33755202469 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 22 -224 2374 -25772 284428 -3176588 35796550 -406214540 4635534292 -53141454896 611540448796 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 9 -224 7825 -354024 19747441 -1311780224 101189138625 -8893436141600 877481411735401 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A100100 | 1 1 1 3 2 1 10 6 3 1 35 20 10 4 1 126 70 35 15 5 1 462 252 126 56 21 6 1 1716 924 462 210 84 28 7 1 |
| Rev | InvT-1(n, k), 0 ≤ k ≤ n | A100218 | 1 -1 1 -1 -2 1 -1 0 -3 1 -1 0 2 -4 1 -1 0 0 5 -5 1 -1 0 0 -2 9 -6 1 -1 0 0 0 -7 14 -7 1 -1 0 0 0 2 |
| Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -2 -1 1 -3 0 -1 1 -4 2 0 -1 1 -5 5 0 0 -1 1 -6 9 -2 0 0 -1 1 -7 14 -7 0 0 0 -1 1 -8 20 -16 |
| Rev | Accsee docs | missing | 1 1 2 3 5 6 10 16 19 20 35 55 65 69 70 126 196 231 246 251 252 462 714 840 896 917 923 924 1716 |
| Rev | AccRevsee docs | A046899 | 1 1 2 1 3 6 1 4 10 20 1 5 15 35 70 1 6 21 56 126 252 1 7 28 84 210 462 924 1 8 36 120 330 792 1716 |
| Rev | AntiDiagsee docs | missing | 1 1 3 1 10 2 35 6 1 126 20 3 462 70 10 1 1716 252 35 4 6435 924 126 15 1 24310 3432 462 56 5 92378 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 3 4 3 10 12 9 4 35 40 30 16 5 126 140 105 60 25 6 462 504 378 224 105 36 7 1716 1848 1386 840 |
| Rev | RowSum∑ k=0..n T(n, k) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A026641 | 1 1 4 13 46 166 610 2269 8518 32206 122464 467842 1794196 6903352 26635774 103020253 399300166 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A014300 | 0 1 2 7 24 86 314 1163 4352 16414 62292 237590 909960 3497248 13480826 52097267 201780224 783051638 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A072547 | 1 0 2 6 22 80 296 1106 4166 15792 60172 230252 884236 3406104 13154948 50922986 197519942 767502944 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A100217 | 1 1 4 12 42 149 543 2007 7501 28265 107196 408653 1564506 6010964 23164467 89501021 346588092 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A034275 | 1 3 14 65 294 1302 5676 24453 104390 442442 1864356 7818538 32657884 135950700 564306840 2336457645 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A001700 | 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 30 140 630 5544 60060 51480 1531530 25865840 23279256 486748080 2230928700 6177956400 |
| 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) | | A001700 | 1 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 2 6 10 35 56 210 330 1287 2002 8008 12376 50388 77520 319770 490314 2042975 3124550 13123110 |
| Rev | CentralET(2 n, n) | A165817 | 1 2 10 56 330 2002 12376 77520 490314 3124550 20030010 129024480 834451800 5414950296 35240152720 |
| Rev | CentralOT(2 n + 1, n) | A117671 | 1 6 35 210 1287 8008 50388 319770 2042975 13123110 84672315 548354040 3562467300 23206929840 |
| Rev | ColLeftT(n, 0) | A001700 | 1 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Rev | 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 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | A002003 | 1 2 8 38 192 1002 5336 28814 157184 864146 4780008 26572086 148321344 830764794 4666890936 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, 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 | TransNat0∑ k=0..n T(n, k) k | A001791 | 0 1 4 15 56 210 792 3003 11440 43758 167960 646646 2496144 9657700 37442160 145422675 565722720 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | A001700 | 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | A220101 | 0 1 6 27 112 450 1782 7007 27456 107406 419900 1641486 6418656 25110020 98285670 384942375 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A119259 | 1 3 17 111 769 5503 40193 297727 2228225 16807935 127574017 973168639 7454392321 57298911231 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -1 9 -61 433 -3141 23145 -172509 1296993 -9817909 74726809 -571326669 4384519441 -33755202469 |
| Rev | 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 |
| Rev | DiagRow2T(n + 2, n) | A000217 | 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 |
| Rev | DiagRow3T(n + 3, n) | A000292 | 10 20 35 56 84 120 165 220 286 364 455 560 680 816 969 1140 1330 1540 1771 2024 2300 2600 2925 3276 |
| Rev | DiagCol1T(n + 1, 1) | A000984 | 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390 |
| Rev | DiagCol2T(n + 2, 2) | A001700 | 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195 |
| Rev | DiagCol3T(n + 3, 3) | A001791 | 1 4 15 56 210 792 3003 11440 43758 167960 646646 2496144 9657700 37442160 145422675 565722720 |
| Rev | Polysee docs | missing | 1 1 1 3 2 1 10 6 3 1 35 20 11 4 1 126 70 42 18 5 1 462 252 163 82 27 6 1 1716 924 638 374 146 38 7 |
| 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 | A059100 | 3 6 11 18 27 38 51 66 83 102 123 146 171 198 227 258 291 326 363 402 443 486 531 578 627 678 731 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 10 20 42 82 146 240 370 542 762 1036 1370 1770 2242 2792 3426 4150 4970 5892 6922 8066 9330 10720 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A032443 | 1 3 11 42 163 638 2510 9908 39203 155382 616666 2449868 9740686 38754732 154276028 614429672 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A100192 | 1 4 18 82 374 1704 7752 35214 159750 723880 3276908 14821668 66991436 302605528 1366182276 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | A293574 | 1 2 11 82 787 9476 139134 2422218 48824675 1118286172 28679699578 814027423892 25330145185646 |
| Rev:Inv | TriangleT(n, k), 0 ≤ k ≤ n | A100218 | 1 -1 1 -1 -2 1 -1 0 -3 1 -1 0 2 -4 1 -1 0 0 5 -5 1 -1 0 0 -2 9 -6 1 -1 0 0 0 -7 14 -7 1 -1 0 0 0 2 |
| Rev:Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -2 -1 1 -3 0 -1 1 -4 2 0 -1 1 -5 5 0 0 -1 1 -6 9 -2 0 0 -1 1 -7 14 -7 0 0 0 -1 1 -8 20 -16 |
| Rev:Inv | InvT-1(n, k), 0 ≤ k ≤ n | A100100 | 1 1 1 3 2 1 10 6 3 1 35 20 10 4 1 126 70 35 15 5 1 462 252 126 56 21 6 1 1716 924 462 210 84 28 7 1 |
| Rev:Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A059481 | 1 1 1 1 2 3 1 3 6 10 1 4 10 20 35 1 5 15 35 70 126 1 6 21 56 126 252 462 1 7 28 84 210 462 924 1716 |
| Rev:Inv | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 -3 2 1 -4 3 0 1 1 0 -2 0 1 9 -5 -5 0 0 1 12 -6 -9 2 0 0 1 6 0 -14 7 0 0 0 1 -15 16 -16 16 -2 |
| Rev:Inv | Accsee docs | missing | 1 -1 0 -1 -3 -2 -1 -1 -4 -3 -1 -1 1 -3 -2 -1 -1 -1 4 -1 0 -1 -1 -1 -3 6 0 1 -1 -1 -1 -1 -8 6 -1 0 |
| Rev:Inv | AccRevsee docs | missing | 1 1 0 1 -1 -2 1 -2 -2 -3 1 -3 -1 -1 -2 1 -4 1 1 1 0 1 -5 4 2 2 2 1 1 -6 8 1 1 1 1 0 1 -7 13 -3 -1 |
| Rev:Inv | AntiDiagsee docs | missing | 1 -1 -1 1 -1 -2 -1 0 1 -1 0 -3 -1 0 2 1 -1 0 0 -4 -1 0 0 5 1 -1 0 0 -2 -5 -1 0 0 0 9 1 -1 0 0 0 -7 |
| Rev:Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 -1 -4 3 -1 0 -9 4 -1 0 6 -16 5 -1 0 0 20 -25 6 -1 0 0 -8 45 -36 7 -1 0 0 0 -35 84 -49 8 -1 0 |
| Rev:Inv | RowSum∑ k=0..n T(n, k) | A100219 | 1 0 -2 -3 -2 0 1 0 -2 -3 -2 0 1 0 -2 -3 -2 0 1 0 -2 -3 -2 0 1 0 -2 -3 -2 0 1 0 -2 -3 -2 0 1 0 -2 -3 |
| Rev:Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 0 -4 2 -6 9 -15 22 -40 60 -100 161 -261 420 -684 1102 -1786 2889 -4675 7562 -12240 19800 |
| Rev:Inv | OddSum∑ k=0..n T(n, k) odd(k) | A366043 | 0 1 -2 1 -4 6 -8 15 -24 37 -62 100 -160 261 -422 681 -1104 1786 -2888 4675 -7564 12237 -19802 32040 |
| Rev:Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A098600 | 1 -2 2 -5 6 -12 17 -30 46 -77 122 -200 321 -522 842 -1365 2206 -3572 5777 -9350 15126 -24477 39602 |
| Rev:Inv | AbsSum∑ k=0..n | T(n, k) | | A001612 | 1 2 4 5 8 12 19 30 48 77 124 200 323 522 844 1365 2208 3572 5779 9350 15128 24477 39604 64080 |
| Rev:Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | A098601 | 1 -1 0 -3 0 -4 2 -5 5 -8 9 -14 16 -24 29 -41 52 -71 92 -124 162 -217 285 -380 501 -666 880 -1168 |
| Rev:Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -6 -9 -6 0 1 -7 -18 -21 -12 0 1 -13 -30 -33 -18 0 1 -19 -42 -45 -24 0 1 -25 -54 -57 -30 0 1 |
| Rev:Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A110666 | 1 1 -2 -6 -6 0 7 7 -2 -12 -12 0 13 13 -2 -18 -18 0 19 19 -2 -24 -24 0 25 25 -2 -30 -30 0 31 31 -2 |
| Rev:Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 3 4 5 18 14 80 270 350 1540 15120 5460 32340 207900 960960 1021020 1621620 2282280 40840800 |
| Rev:Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A014963 | 1 1 2 3 2 5 1 7 2 3 1 11 1 13 1 1 2 17 1 19 1 1 1 23 1 5 1 3 1 29 1 31 2 1 1 1 1 37 1 1 1 41 1 43 1 |
| Rev:Inv | RowMaxMax k=0..n | T(n, k) | | A277282 | 1 1 2 3 4 5 9 14 20 30 50 77 112 182 294 450 672 1122 1782 2717 4290 7007 11011 16744 27456 44200 |
| Rev:Inv | ColMiddleT(n, n // 2) | A267602 | 1 -1 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 |
| Rev:Inv | CentralET(2 n, n) | A055642 | 1 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 2 -2 |
| Rev:Inv | CentralOT(2 n + 1, n) | 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 |
| Rev:Inv | 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 |
| Rev: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 |
| Rev:Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 -9 -4 25 59 0 -260 -495 221 2662 4091 -4394 -27444 -32609 65276 280041 236741 -864234 |
| Rev:Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 4 11 28 77 211 590 1660 4709 13429 38480 110683 319412 924340 2681411 7794940 22702397 66229213 |
| Rev:Inv | TransNat0∑ k=0..n T(n, k) k | A110665 | 0 1 0 -3 -4 0 6 7 0 -9 -10 0 12 13 0 -15 -16 0 18 19 0 -21 -22 0 24 25 0 -27 -28 0 30 31 0 -33 -34 |
| Rev:Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | A110666 | 1 1 -2 -6 -6 0 7 7 -2 -12 -12 0 13 13 -2 -18 -18 0 19 19 -2 -24 -24 0 25 25 -2 -30 -30 0 31 31 -2 |
| Rev:Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 2 -3 -12 -10 12 35 24 -27 -70 -44 48 117 70 -75 -176 -102 108 247 140 -147 -330 -184 192 425 |
| Rev:Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 -7 -13 -15 -21 -55 -141 -287 -517 -967 -1981 -4143 -8373 -16471 -32493 -65087 -131173 -263143 |
| Rev:Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A080924 | 1 3 1 15 1 63 1 255 1 1023 1 4095 1 16383 1 65535 1 262143 1 1048575 1 4194303 1 16777215 1 |
| Rev: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 |
| Rev:Inv | DiagRow2T(n + 2, n) | A000096 | -1 0 2 5 9 14 20 27 35 44 54 65 77 90 104 119 135 152 170 189 209 230 252 275 299 324 350 377 405 |
| Rev:Inv | DiagRow3T(n + 3, n) | A005581 | -1 0 0 -2 -7 -16 -30 -50 -77 -112 -156 -210 -275 -352 -442 -546 -665 -800 -952 -1122 -1311 -1520 |
| Rev:Inv | DiagCol1T(n + 1, 1) | A130706 | 1 -2 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:Inv | Polysee docs | missing | 1 -1 1 -1 0 1 -1 -2 1 1 -1 -3 -1 2 1 -1 -2 -5 2 3 1 -1 0 -9 -1 7 4 1 -1 1 -9 -10 15 14 5 1 -1 0 -1 |
| Rev: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 |
| Rev:Inv | PolyRow2∑ k=0..2 T(2, k) n^k | A008865 | -1 -2 -1 2 7 14 23 34 47 62 79 98 119 142 167 194 223 254 287 322 359 398 439 482 527 574 623 674 |
| Rev:Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -1 -3 -5 -1 15 49 107 195 319 485 699 967 1295 1689 2155 2699 3327 4045 4859 5775 6799 7937 9195 |
| Rev:Inv | PolyCol2∑ k=0..n T(n, k) 2^k | A321632 | 1 1 -1 -5 -9 -9 -1 15 31 31 -1 -65 -129 -129 -1 255 511 511 -1 -1025 -2049 -2049 -1 4095 8191 8191 |
| Rev:Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 2 -1 -10 -28 -55 -82 -82 -1 242 728 1457 2186 2186 -1 -6562 -19684 -39367 -59050 -59050 -1 |
| Rev:Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -1 -1 31 624 11231 218490 4726783 113728373 3024799999 88296371800 2809506373631 96841104004956 |
| << | 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.