OEIS Similars: A367564
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A367564 | 1 1 1 3 2 1 7 9 3 1 17 28 18 4 1 41 85 70 30 5 1 99 246 255 140 45 6 1 239 693 861 595 245 63 7 1 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 1 1 2 3 1 3 9 7 1 4 18 28 17 1 5 30 70 85 41 1 6 45 140 255 246 99 1 7 63 245 595 861 693 239 1 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -1 -2 1 5 -3 -3 1 9 20 -6 -4 1 -81 45 50 -10 -5 1 -217 -486 135 100 -15 -6 1 2757 -1519 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -2 -1 1 -3 -3 5 1 -4 -6 20 9 1 -5 -10 50 45 -81 1 -6 -15 100 135 -486 -217 1 -7 -21 175 |
| Std | Accsee docs | missing | 1 1 2 3 5 6 7 16 19 20 17 45 63 67 68 41 126 196 226 231 232 99 345 600 740 785 791 792 239 932 |
| Std | AccRevsee docs | missing | 1 1 2 1 3 6 1 4 13 20 1 5 23 51 68 1 6 36 106 191 232 1 7 52 192 447 693 792 1 8 71 316 911 1772 |
| Std | AntiDiagsee docs | missing | 1 1 3 1 7 2 17 9 1 41 28 3 99 85 18 1 239 246 70 4 577 693 255 30 1 1393 1912 861 140 5 3363 5193 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 3 4 3 7 18 9 4 17 56 54 16 5 41 170 210 120 25 6 99 492 765 560 225 36 7 239 1386 2583 2380 |
| Std | RowSum∑ k=0..n T(n, k) | A006012 | 1 2 6 20 68 232 792 2704 9232 31520 107616 367424 1254464 4283008 14623104 49926400 170459392 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A088013 | 1 1 4 10 36 116 400 1352 4624 15760 53824 183712 627264 2141504 7311616 24963200 85229824 290992384 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A084154 | 0 1 2 10 32 116 392 1352 4608 15760 53792 183712 627200 2141504 7311488 24963200 85229568 290992384 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A077957 | 1 0 2 0 4 0 8 0 16 0 32 0 64 0 128 0 256 0 512 0 1024 0 2048 0 4096 0 8192 0 16384 0 32768 0 65536 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A006012 | 1 2 6 20 68 232 792 2704 9232 31520 107616 367424 1254464 4283008 14623104 49926400 170459392 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 4 9 27 72 203 559 1556 4311 11969 33200 92129 255609 709236 1967841 5460043 15149528 42034267 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 14 62 260 1052 4152 16088 61456 232112 868576 3225312 11898944 43654080 159384448 579475840 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 10 38 148 572 2184 8248 30864 114608 422816 1551200 5663552 20591040 74585216 269272960 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 63 4284 146370 9660420 4040470665 18650812589640 1113453511601508 1783116266436129240 |
| 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 3 9 28 85 255 861 2772 8604 28680 95205 306460 995995 3366363 11082435 35673820 121290988 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 2 9 18 70 140 595 1190 5166 10332 45738 91476 410124 820248 3712995 7425990 33863830 67727660 |
| Std | CentralET(2 n, n) | missing | 1 2 18 140 1190 10332 91476 820248 7425990 67727660 621334428 5727402408 53004161756 492166792600 |
| Std | CentralOT(2 n + 1, n) | missing | 1 9 70 595 5166 45738 410124 3712995 33863830 310667214 2863701204 26502080878 246083396300 |
| Std | ColLeftT(n, 0) | A001333 | 1 1 3 7 17 41 99 239 577 1393 3363 8119 19601 47321 114243 275807 665857 1607521 3880899 9369319 |
| 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 8 44 254 1492 8912 53944 329734 2030588 12578928 78298024 489313772 3068183848 19293898912 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 0 12 -2 -40 288 56 -2042 7536 8000 -83864 187372 511056 -3114048 3758192 25837638 -106646304 |
| Std | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 4 18 80 340 1392 5544 21632 83088 315200 1183776 4409088 16308032 59962112 219346560 798822400 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 10 38 148 572 2184 8248 30864 114608 422816 1551200 5663552 20591040 74585216 269272960 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 6 30 152 740 3432 15288 65984 277776 1146080 4650976 18614400 73626176 288274560 1118778240 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A001541 | 1 3 17 99 577 3363 19601 114243 665857 3880899 22619537 131836323 768398401 4478554083 26102926097 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A083100 | 1 -1 9 -25 113 -401 1593 -5993 23137 -88225 338409 -1294393 4957649 -18976049 72655641 -278143625 |
| 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) | A045943 | 3 9 18 30 45 63 84 108 135 165 198 234 273 315 360 408 459 513 570 630 693 759 828 900 975 1053 |
| Std | DiagRow3T(n + 3, n) | missing | 7 28 70 140 245 392 588 840 1155 1540 2002 2548 3185 3920 4760 5712 6783 7980 9310 10780 12397 |
| Std | DiagCol1T(n + 1, 1) | missing | 1 2 9 28 85 246 693 1912 5193 13930 36993 97428 254813 662494 1713645 4412912 11319569 28935378 |
| Std | DiagCol2T(n + 2, 2) | missing | 1 3 18 70 255 861 2772 8604 25965 76615 221958 633282 1783691 4968705 13709160 37509752 101876121 |
| Std | DiagCol3T(n + 3, 3) | missing | 1 4 30 140 595 2296 8316 28680 95205 306460 961818 2955316 8918455 26499760 77685240 225058512 |
| Std | Polysee docs | missing | 1 1 1 3 2 1 7 6 3 1 17 20 11 4 1 41 68 45 18 5 1 99 232 193 88 27 6 1 239 792 843 452 155 38 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 | 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 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 7 20 45 88 155 252 385 560 783 1060 1397 1800 2275 2828 3465 4192 5015 5940 6973 8120 9387 10780 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A083878 | 1 3 11 45 193 843 3707 16341 72097 318195 1404491 6199581 27366049 120799227 533233019 2353803525 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A083879 | 1 4 18 88 452 2384 12744 68576 370192 2001472 10829088 58612096 317289536 1717746944 9299922048 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 11 88 929 12216 192627 3545536 74662657 1771073440 46742519163 1358806445184 43146459206369 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A367564 | 1 1 -1 3 -2 1 7 -9 3 -1 17 -28 18 -4 1 41 -85 70 -30 5 -1 99 -246 255 -140 45 -6 1 239 -693 861 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 1 1 -2 3 -1 3 -9 7 1 -4 18 -28 17 -1 5 -30 70 -85 41 1 -6 45 -140 255 -246 99 -1 7 -63 245 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -5 2 1 -1 3 -3 1 41 4 -30 4 1 -11 15 -10 10 -5 1 -1121 66 615 20 -75 6 1 -113 259 -231 105 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 2 -5 1 -3 3 -1 1 4 -30 4 41 1 -5 10 -10 15 -11 1 6 -75 20 615 66 -1121 1 -7 21 -35 105 |
| Alt | Accsee docs | missing | 1 1 0 3 1 2 7 -2 1 0 17 -11 7 3 4 41 -44 26 -4 1 0 99 -147 108 -32 13 7 8 239 -454 407 -188 57 -6 1 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -1 2 -1 2 -7 0 1 -3 15 -13 4 -1 4 -26 44 -41 0 1 -5 40 -100 155 -91 8 -1 6 -57 188 -407 |
| Alt | AntiDiagsee docs | missing | 1 1 3 -1 7 -2 17 -9 1 41 -28 3 99 -85 18 -1 239 -246 70 -4 577 -693 255 -30 1 1393 -1912 861 -140 5 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 3 -4 3 7 -18 9 -4 17 -56 54 -16 5 41 -170 210 -120 25 -6 99 -492 765 -560 225 -36 7 239 |
| Alt | RowSum∑ k=0..n T(n, k) | A077957 | 1 0 2 0 4 0 8 0 16 0 32 0 64 0 128 0 256 0 512 0 1024 0 2048 0 4096 0 8192 0 16384 0 32768 0 65536 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A088013 | 1 1 4 10 36 116 400 1352 4624 15760 53824 183712 627264 2141504 7311616 24963200 85229824 290992384 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A084154 | 0 -1 -2 -10 -32 -116 -392 -1352 -4608 -15760 -53792 -183712 -627200 -2141504 -7311488 -24963200 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A006012 | 1 2 6 20 68 232 792 2704 9232 31520 107616 367424 1254464 4283008 14623104 49926400 170459392 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A006012 | 1 2 6 20 68 232 792 2704 9232 31520 107616 367424 1254464 4283008 14623104 49926400 170459392 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 5 9 16 31 59 110 207 391 736 1385 2609 4914 9253 17425 32816 61799 116379 219166 412735 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 6 6 20 20 56 56 144 144 352 352 832 832 1920 1920 4352 4352 9728 9728 21504 21504 47104 47104 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 2 -6 4 -20 8 -56 16 -144 32 -352 64 -832 128 -1920 256 -4352 512 -9728 1024 -21504 2048 -47104 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 63 4284 146370 9660420 4040470665 18650812589640 1113453511601508 1783116266436129240 |
| 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 3 9 28 85 255 861 2772 8604 28680 95205 306460 995995 3366363 11082435 35673820 121290988 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -2 -9 18 70 -140 -595 1190 5166 -10332 -45738 91476 410124 -820248 -3712995 7425990 33863830 |
| Alt | CentralET(2 n, n) | missing | 1 -2 18 -140 1190 -10332 91476 -820248 7425990 -67727660 621334428 -5727402408 53004161756 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 -9 70 -595 5166 -45738 410124 -3712995 33863830 -310667214 2863701204 -26502080878 246083396300 |
| Alt | ColLeftT(n, 0) | A001333 | 1 1 3 7 17 41 99 239 577 1393 3363 8119 19601 47321 114243 275807 665857 1607521 3880899 9369319 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 0 -12 -2 40 288 -56 -2042 -7536 8000 83864 187372 -511056 -3114048 -3758192 25837638 106646304 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 8 -44 254 -1492 8912 -53944 329734 -2030588 12578928 -78298024 489313772 -3068183848 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A014480 | 0 -1 0 -6 0 -20 0 -56 0 -144 0 -352 0 -832 0 -1920 0 -4352 0 -9728 0 -21504 0 -47104 0 -102400 0 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 2 -6 4 -20 8 -56 16 -144 32 -352 64 -832 128 -1920 256 -4352 512 -9728 1024 -21504 2048 -47104 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 2 -6 24 -20 120 -56 448 -144 1440 -352 4224 -832 11648 -1920 30720 -4352 78336 -9728 194560 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A083100 | 1 1 9 25 113 401 1593 5993 23137 88225 338409 1294393 4957649 18976049 72655641 278143625 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001541 | 1 -3 17 -99 577 -3363 19601 -114243 665857 -3880899 22619537 -131836323 768398401 -4478554083 |
| 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) | A045943 | 3 -9 18 -30 45 -63 84 -108 135 -165 198 -234 273 -315 360 -408 459 -513 570 -630 693 -759 828 -900 |
| Alt | DiagRow3T(n + 3, n) | missing | 7 -28 70 -140 245 -392 588 -840 1155 -1540 2002 -2548 3185 -3920 4760 -5712 6783 -7980 9310 -10780 |
| Alt | DiagCol1T(n + 1, 1) | missing | -1 -2 -9 -28 -85 -246 -693 -1912 -5193 -13930 -36993 -97428 -254813 -662494 -1713645 -4412912 |
| Alt | DiagCol2T(n + 2, 2) | missing | 1 3 18 70 255 861 2772 8604 25965 76615 221958 633282 1783691 4968705 13709160 37509752 101876121 |
| Alt | DiagCol3T(n + 3, 3) | missing | -1 -4 -30 -140 -595 -2296 -8316 -28680 -95205 -306460 -961818 -2955316 -8918455 -26499760 -77685240 |
| Alt | Polysee docs | missing | 1 1 1 3 0 1 7 2 -1 1 17 0 3 -2 1 41 4 -7 6 -3 1 99 0 17 -20 11 -4 1 239 8 -41 68 -45 18 -5 1 577 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 | A059100 | 3 2 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 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 7 0 -7 -20 -45 -88 -155 -252 -385 -560 -783 -1060 -1397 -1800 -2275 -2828 -3465 -4192 -5015 -5940 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A001333 | 1 -1 3 -7 17 -41 99 -239 577 -1393 3363 -8119 19601 -47321 114243 -275807 665857 -1607521 3880899 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A006012 | 1 -2 6 -20 68 -232 792 -2704 9232 -31520 107616 -367424 1254464 -4283008 14623104 -49926400 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 3 -20 193 -2384 35883 -637104 13036417 -302072960 7818480563 -223572243520 6999810599681 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 1 1 2 3 1 3 9 7 1 4 18 28 17 1 5 30 70 85 41 1 6 45 140 255 246 99 1 7 63 245 595 861 693 239 1 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 -1 -2 1 5 -3 -3 1 9 20 -6 -4 1 -81 45 50 -10 -5 1 -217 -486 135 100 -15 -6 1 2757 -1519 |
| Rev | Accsee docs | missing | 1 1 2 1 3 6 1 4 13 20 1 5 23 51 68 1 6 36 106 191 232 1 7 52 192 447 693 792 1 8 71 316 911 1772 |
| Rev | AccRevsee docs | missing | 1 1 2 3 5 6 7 16 19 20 17 45 63 67 68 41 126 196 226 231 232 99 345 600 740 785 791 792 239 932 |
| Rev | AntiDiagsee docs | missing | 1 1 1 1 1 2 1 3 3 1 4 9 1 5 18 7 1 6 30 28 1 7 45 70 17 1 8 63 140 85 1 9 84 245 255 41 1 10 108 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 4 9 1 6 27 28 1 8 54 112 85 1 10 90 280 425 246 1 12 135 560 1275 1476 693 1 14 189 980 |
| Rev | RowSum∑ k=0..n T(n, k) | A006012 | 1 2 6 20 68 232 792 2704 9232 31520 107616 367424 1254464 4283008 14623104 49926400 170459392 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A088013 | 1 1 4 10 36 116 400 1352 4624 15760 53824 183712 627264 2141504 7311616 24963200 85229824 290992384 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A084154 | 0 1 2 10 32 116 392 1352 4608 15760 53792 183712 627200 2141504 7311488 24963200 85229568 290992384 |
| Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A077957 | 1 0 2 0 4 0 8 0 16 0 32 0 64 0 128 0 256 0 512 0 1024 0 2048 0 4096 0 8192 0 16384 0 32768 0 65536 |
| Rev | AbsSum∑ k=0..n | T(n, k) | | A006012 | 1 2 6 20 68 232 792 2704 9232 31520 107616 367424 1254464 4283008 14623104 49926400 170459392 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 2 3 7 14 31 65 140 297 635 1352 2885 6149 13114 27959 59619 127118 271051 577941 1232316 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 10 38 148 572 2184 8248 30864 114608 422816 1551200 5663552 20591040 74585216 269272960 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 14 62 260 1052 4152 16088 61456 232112 868576 3225312 11898944 43654080 159384448 579475840 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 63 4284 146370 9660420 4040470665 18650812589640 1113453511601508 1783116266436129240 |
| 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 3 9 28 85 255 861 2772 8604 28680 95205 306460 995995 3366363 11082435 35673820 121290988 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 2 3 18 30 140 245 1190 2142 10332 18942 91476 169884 820248 1537965 7425990 14026870 67727660 |
| Rev | CentralET(2 n, n) | missing | 1 2 18 140 1190 10332 91476 820248 7425990 67727660 621334428 5727402408 53004161756 492166792600 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 3 30 245 2142 18942 169884 1537965 14026870 128682554 1186183908 10977521282 101931080300 |
| 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) | A001333 | 1 1 3 7 17 41 99 239 577 1393 3363 8119 19601 47321 114243 275807 665857 1607521 3880899 9369319 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 8 44 254 1492 8912 53944 329734 2030588 12578928 78298024 489313772 3068183848 19293898912 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 0 -12 -2 40 288 -56 -2042 -7536 8000 83864 187372 -511056 -3114048 -3758192 25837638 106646304 |
| Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 8 42 192 820 3360 13384 52224 200592 760960 2857888 10644480 39371072 144761344 529549440 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 14 62 260 1052 4152 16088 61456 232112 868576 3225312 11898944 43654080 159384448 579475840 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 14 102 600 3140 15240 70168 310720 1335312 5603680 23066208 93439104 373445696 1475463808 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A083878 | 1 3 11 45 193 843 3707 16341 72097 318195 1404491 6199581 27366049 120799227 533233019 2353803525 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001333 | 1 -1 3 -7 17 -41 99 -239 577 -1393 3363 -8119 19601 -47321 114243 -275807 665857 -1607521 3880899 |
| Rev | DiagRow1T(n + 1, n) | missing | 1 2 9 28 85 246 693 1912 5193 13930 36993 97428 254813 662494 1713645 4412912 11319569 28935378 |
| Rev | DiagRow2T(n + 2, n) | missing | 1 3 18 70 255 861 2772 8604 25965 76615 221958 633282 1783691 4968705 13709160 37509752 101876121 |
| Rev | DiagRow3T(n + 3, n) | missing | 1 4 30 140 595 2296 8316 28680 95205 306460 961818 2955316 8918455 26499760 77685240 225058512 |
| 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) | A045943 | 3 9 18 30 45 63 84 108 135 165 198 234 273 315 360 408 459 513 570 630 693 759 828 900 975 1053 |
| Rev | DiagCol3T(n + 3, 3) | missing | 7 28 70 140 245 392 588 840 1155 1540 2002 2548 3185 3920 4760 5712 6783 7980 9310 10780 12397 |
| Rev | Polysee docs | missing | 1 1 1 1 2 1 1 6 3 1 1 20 17 4 1 1 68 99 34 5 1 1 232 577 280 57 6 1 1 792 3363 2308 605 86 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 | 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 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 20 99 280 605 1116 1855 2864 4185 5860 7931 10440 13429 16940 21015 25696 31025 37044 43795 51320 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A001541 | 1 3 17 99 577 3363 19601 114243 665857 3880899 22619537 131836323 768398401 4478554083 26102926097 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 34 280 2308 19024 156808 1292512 10653712 87814720 723825184 5966230912 49177497664 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 17 280 6449 190776 6894217 294344128 14497187137 809110030240 50465159753601 3478631916722304 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -1 -2 1 5 -3 -3 1 9 20 -6 -4 1 -81 45 50 -10 -5 1 -217 -486 135 100 -15 -6 1 2757 -1519 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -2 -1 1 -3 -3 5 1 -4 -6 20 9 1 -5 -10 50 45 -81 1 -6 -15 100 135 -486 -217 1 -7 -21 175 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 1 1 2 3 1 3 9 7 1 4 18 28 17 1 5 30 70 85 41 1 6 45 140 255 246 99 1 7 63 245 595 861 693 239 1 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -1 -2 1 -2 -5 0 1 -3 -9 11 20 1 -4 -14 36 81 0 1 -5 -20 80 215 -271 -488 1 -6 -27 148 463 |
| Inv | AntiDiagsee docs | missing | 1 -1 -1 1 5 -2 9 -3 1 -81 20 -3 -217 45 -6 1 2757 -486 50 -4 9841 -1519 135 -10 1 -160897 22056 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 -1 -4 3 5 -6 -9 4 9 40 -18 -16 5 -81 90 150 -40 -25 6 -217 -972 405 400 -75 -36 7 2757 -3038 |
| Inv | RowSum∑ k=0..n T(n, k) | A012816 | 1 0 -2 0 20 0 -488 0 22160 0 -1616672 0 172976960 0 -25518205568 0 4964227109120 0 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 0 2 4 -36 -96 1224 4368 -71440 -318720 6369824 34102336 -805457472 -5030914560 137104651392 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -2 -2 16 36 -392 -1224 17792 71440 -1297952 -6369824 138874624 805457472 -20487291008 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -2 2 4 -12 -72 296 2448 -13424 -142880 979232 12739648 -104772288 -1610914944 15456376448 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 4 12 40 192 960 6496 43456 378752 3169024 33766656 339056128 4269699072 50018562048 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 0 3 7 -64 -177 2317 8448 -140447 -635047 12831872 69333641 -1650405889 -10377827584 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -2 -6 20 100 -488 -3416 22160 199440 -1616672 -17783392 172976960 2248700480 -25518205568 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 15 180 4050 5273100 8480463075 44509993131240 32226859641767050260 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 5 20 81 486 2757 22056 160897 1608970 14345957 172151484 1814028945 25396405230 308783248485 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -2 -3 -6 50 100 315 630 -10206 -20412 -100254 -200508 4731012 9462024 63326835 126653670 |
| Inv | CentralET(2 n, n) | missing | 1 -2 -6 100 630 -20412 -200508 9462024 126653670 -7822812140 -132625431796 10120097138424 |
| Inv | CentralOT(2 n + 1, n) | missing | -1 -3 50 315 -10206 -100254 4731012 63326835 -3911406070 -66312715898 5060048569212 103845897843870 |
| Inv | ColLeftT(n, 0) | missing | 1 -1 -1 5 9 -81 -217 2757 9841 -160897 -717841 14345957 76804665 -1814028945 -11330490025 |
| 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 -4 -12 38 520 632 -26936 -178922 1568976 28574536 -53560936 -4864684900 -18873738000 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 4 -4 -90 -268 2536 26840 -55018 -2753860 -8503816 325005320 3220908444 -41267466264 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 0 -6 0 100 0 -3416 0 199440 0 -17783392 0 2248700480 0 -382773083520 0 84391860855040 0 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -2 -6 20 100 -488 -3416 22160 199440 -1616672 -17783392 172976960 2248700480 -25518205568 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 2 -6 -24 100 600 -3416 -27328 199440 1994400 -17783392 -213400704 2248700480 31481806720 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 -7 23 273 -1521 -26551 207591 4820641 -48473185 -1406680807 17288479031 602031882417 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 3 1 -45 -31 2883 2977 -392109 -539839 91523331 157506241 -32641371309 -67408618975 16509827111235 |
| 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 | DiagRow2T(n + 2, n) | A000217 | -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 -276 |
| Inv | 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 |
| Inv | DiagCol1T(n + 1, 1) | missing | 1 -2 -3 20 45 -486 -1519 22056 88569 -1608970 -7896251 172151484 998460645 -25396405230 |
| Inv | DiagCol2T(n + 2, 2) | missing | 1 -3 -6 50 135 -1701 -6076 99252 442845 -8849335 -47377506 1118984646 6989224515 -190473039225 |
| Inv | DiagCol3T(n + 3, 3) | missing | 1 -4 -10 100 315 -4536 -18228 330840 1623765 -35397340 -205302526 5221928348 34946122575 |
| Inv | Polysee docs | missing | 1 -1 1 -1 0 1 5 -2 1 1 9 0 -1 2 1 -81 20 -5 2 3 1 -217 0 9 -4 7 4 1 2757 -488 81 -12 9 14 5 1 9841 |
| 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 | 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 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 5 0 -5 -4 9 40 95 180 301 464 675 940 1265 1656 2119 2660 3285 4000 4811 5724 6745 7880 9135 10516 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 -1 -5 9 81 -217 -2757 9841 160897 -717841 -14345957 76804665 1814028945 -11330490025 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 2 -4 -12 72 296 -2448 -13424 142880 979232 -12739648 -104772288 1610914944 15456376448 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -1 -4 -7 144 3887 84048 1890481 46405760 1251416959 36932966080 1185885429225 41187596815104 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -2 -1 1 -3 -3 5 1 -4 -6 20 9 1 -5 -10 50 45 -81 1 -6 -15 100 135 -486 -217 1 -7 -21 175 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 -1 1 -1 -2 1 5 -3 -3 1 9 20 -6 -4 1 -81 45 50 -10 -5 1 -217 -486 135 100 -15 -6 1 2757 -1519 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A367564 | 1 1 1 3 2 1 7 9 3 1 17 28 18 4 1 41 85 70 30 5 1 99 246 255 140 45 6 1 239 693 861 595 245 63 7 1 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -1 -2 1 -2 -5 0 1 -3 -9 11 20 1 -4 -14 36 81 0 1 -5 -20 80 215 -271 -488 1 -6 -27 148 463 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -2 1 -3 -1 1 -4 -3 1 -5 -6 5 1 -6 -10 20 1 -7 -15 50 9 1 -8 -21 100 45 1 -9 -28 175 135 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A012816 | 1 0 -2 0 20 0 -488 0 22160 0 -1616672 0 172976960 0 -25518205568 0 4964227109120 0 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 0 -2 4 36 -96 -1224 4368 71440 -318720 -6369824 34102336 805457472 -5030914560 -137104651392 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -2 2 16 -36 -392 1224 17792 -71440 -1297952 6369824 138874624 -805457472 -20487291008 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 2 2 -4 -12 72 296 -2448 -13424 142880 979232 -12739648 -104772288 1610914944 15456376448 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 4 12 40 192 960 6496 43456 378752 3169024 33766656 339056128 4269699072 50018562048 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -1 -3 -6 -5 5 38 117 193 64 -923 -4387 -10888 -12605 31881 263138 898151 1678737 -840154 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -2 -6 20 100 -488 -3416 22160 199440 -1616672 -17783392 172976960 2248700480 -25518205568 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 2 15 180 4050 5273100 8480463075 44509993131240 32226859641767050260 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A000012 | 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 2 5 20 81 486 2757 22056 160897 1608970 14345957 172151484 1814028945 25396405230 308783248485 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -2 -3 -6 -10 100 175 630 1134 -20412 -37422 -200508 -372372 9462024 17741295 126653670 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 -2 -6 100 630 -20412 -200508 9462024 126653670 -7822812140 -132625431796 10120097138424 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -3 -10 175 1134 -37422 -372372 17741295 239234710 -14863343066 -253194006156 19396852848646 |
| 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 -1 -1 5 9 -81 -217 2757 9841 -160897 -717841 14345957 76804665 -1814028945 -11330490025 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 -12 38 520 632 -26936 -178922 1568976 28574536 -53560936 -4864684900 -18873738000 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 4 4 -90 268 2536 -26840 -55018 2753860 -8503816 -325005320 3220908444 41267466264 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 -4 6 80 -100 -2928 3416 177280 -199440 -16166720 17783392 2075723520 -2248700480 -357254877952 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 -6 30 296 -900 -16968 44408 1390912 -3390480 -159672800 373451232 24695281536 -56217512000 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -1 -5 9 81 -217 -2757 9841 160897 -717841 -14345957 76804665 1814028945 -11330490025 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -3 7 -9 -7 -3 511 -633 -21679 33885 1587607 -3033033 -169844983 383484189 25056238543 |
| Inv:Rev | DiagRow1T(n + 1, n) | missing | 1 -2 -3 20 45 -486 -1519 22056 88569 -1608970 -7896251 172151484 998460645 -25396405230 |
| Inv:Rev | DiagRow2T(n + 2, n) | missing | 1 -3 -6 50 135 -1701 -6076 99252 442845 -8849335 -47377506 1118984646 6989224515 -190473039225 |
| Inv:Rev | DiagRow3T(n + 3, n) | missing | 1 -4 -10 100 315 -4536 -18228 330840 1623765 -35397340 -205302526 5221928348 34946122575 |
| 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 | DiagCol2T(n + 2, 2) | A000217 | -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253 -276 |
| Inv: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 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 -2 -1 1 1 0 -7 -2 1 1 20 23 -14 -3 1 1 0 273 100 -23 -4 1 1 -488 -1521 1204 261 -34 |
| 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 | A008865 | 1 -2 -7 -14 -23 -34 -47 -62 -79 -98 -119 -142 -167 -194 -223 -254 -287 -322 -359 -398 -439 -482 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 0 23 100 261 536 955 1548 2345 3376 4671 6260 8173 10440 13091 16156 19665 23648 28135 33156 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -1 -7 23 273 -1521 -26551 207591 4820641 -48473185 -1406680807 17288479031 602031882417 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 -14 100 1204 -14792 -262808 4538896 107329936 -2384435744 -70466108384 1913457418816 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -7 100 3473 -219024 -13707503 2064025776 209620666561 -58057752164480 -8739834691704599 |
| << | 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.