OEIS Similars: A060187, A138076
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A060187 | 1 1 1 1 6 1 1 23 23 1 1 76 230 76 1 1 237 1682 1682 237 1 1 722 10543 23548 10543 722 1 1 2179 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A060187 | 1 1 1 1 6 1 1 23 23 1 1 76 230 76 1 1 237 1682 1682 237 1 1 722 10543 23548 10543 722 1 1 2179 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A171273 | 1 -1 1 5 -6 1 -93 115 -23 1 5993 -7436 1518 -76 1 -1272089 1578757 -322762 16330 -237 1 857402029 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -6 5 1 -23 115 -93 1 -76 1518 -7436 5993 1 -237 16330 -322762 1578757 -1272089 1 -722 |
| Std | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A171273 | 1 -1 1 5 -6 1 -93 115 -23 1 5993 -7436 1518 -76 1 -1272089 1578757 -322762 16330 -237 1 857402029 |
| Std | Accsee docs | missing | 1 1 2 1 7 8 1 24 47 48 1 77 307 383 384 1 238 1920 3602 3839 3840 1 723 11266 34814 45357 46079 |
| Std | AccRevsee docs | missing | 1 1 2 1 7 8 1 24 47 48 1 77 307 383 384 1 238 1920 3602 3839 3840 1 723 11266 34814 45357 46079 |
| Std | AntiDiagsee docs | missing | 1 1 1 1 1 6 1 23 1 1 76 23 1 237 230 1 1 722 1682 76 1 2179 10543 1682 1 1 6552 60657 23548 237 1 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 12 3 1 46 69 4 1 152 690 304 5 1 474 5046 6728 1185 6 1 1444 31629 94192 52715 4332 7 1 |
| Std | RowSum∑ k=0..n T(n, k) | A000165 | 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 2 24 232 1920 21088 322560 5338240 92897280 1832078848 40874803200 986530539520 25505877196800 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 6 24 152 1920 24992 322560 4983680 92897280 1883812352 40874803200 975460014080 25505877196800 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A002436 | 1 0 -4 0 80 0 -3904 0 354560 0 -51733504 0 11070525440 0 -3266330312704 0 1270842139934720 0 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000165 | 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A178118 | 1 1 2 7 25 100 469 2481 14406 90995 621553 4561112 35736921 297435521 2618575194 24297706927 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A187735 | 1 3 16 120 1152 13440 184320 2903040 51609600 1021870080 22295347200 531372441600 13733933875200 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A187735 | 1 3 16 120 1152 13440 184320 2903040 51609600 1021870080 22295347200 531372441600 13733933875200 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 23 8740 398634 89624229604 34328005245969 3371304106638422136 6508053348450890352622220 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 6 23 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Std | RowMaxMax k=0..n | T(n, k) | | A154420 | 1 1 6 23 230 1682 23548 259723 4675014 69413294 1527092468 28588019814 743288515164 16818059163492 |
| Std | ColMiddleT(n, n // 2) | A154420 | 1 1 6 23 230 1682 23548 259723 4675014 69413294 1527092468 28588019814 743288515164 16818059163492 |
| Std | CentralET(2 n, n) | A177043 | 1 6 230 23548 4675014 1527092468 743288515164 504541774904760 455522635895576646 |
| Std | CentralOT(2 n + 1, n) | missing | 1 23 1682 259723 69413294 28588019814 16818059163492 13397724585164019 13892023109165902550 |
| 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) | 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 14 140 1990 36012 795916 20758712 624278342 21265899980 809348930788 34035791356008 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -10 0 774 0 -163332 0 67364166 0 -45892468524 0 46687337311900 0 -66323461965129160 0 |
| Std | TransNat0∑ k=0..n T(n, k) k | A014479 | 0 1 8 72 768 9600 138240 2257920 41287680 836075520 18579456000 449622835200 11771943321600 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A187735 | 1 3 16 120 1152 13440 184320 2903040 51609600 1021870080 22295347200 531372441600 13733933875200 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 10 124 1696 25920 441600 8332800 172892160 3917168640 96303513600 2554675200000 72757149696000 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A080253 | 1 3 17 147 1697 24483 423857 8560947 197613377 5131725123 148070287697 4699645934547 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -1 -7 39 177 -3441 -2007 514359 -2913183 -107756001 1777832793 25512663879 -1062285896943 |
| Std | DiagRow1T(n + 1, n) | A060188 | 1 6 23 76 237 722 2179 6552 19673 59038 177135 531428 1594309 4782954 14348891 43046704 129140145 |
| Std | DiagRow2T(n + 2, n) | A060189 | 1 23 230 1682 10543 60657 331612 1756340 9116141 46702427 237231970 1198382694 6031771195 |
| Std | DiagRow3T(n + 3, n) | A060190 | 1 76 1682 23548 259723 2485288 21707972 178300904 1403080725 10708911188 79944249686 587172549764 |
| Std | DiagCol1T(n + 1, 1) | A060188 | 1 6 23 76 237 722 2179 6552 19673 59038 177135 531428 1594309 4782954 14348891 43046704 129140145 |
| Std | DiagCol2T(n + 2, 2) | A060189 | 1 23 230 1682 10543 60657 331612 1756340 9116141 46702427 237231970 1198382694 6031771195 |
| Std | DiagCol3T(n + 3, 3) | A060190 | 1 76 1682 23548 259723 2485288 21707972 178300904 1403080725 10708911188 79944249686 587172549764 |
| Std | Polysee docs | missing | 1 1 1 1 2 1 1 8 3 1 1 48 17 4 1 1 384 147 28 5 1 1 3840 1697 304 41 6 1 1 46080 24483 4432 525 56 7 |
| 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 | A028884 | 1 8 17 28 41 56 73 92 113 136 161 188 217 248 281 316 353 392 433 476 521 568 617 668 721 776 833 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 48 147 304 525 816 1183 1632 2169 2800 3531 4368 5317 6384 7575 8896 10353 11952 13699 15600 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A080253 | 1 3 17 147 1697 24483 423857 8560947 197613377 5131725123 148070287697 4699645934547 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 4 28 304 4432 80704 1763008 44932864 1308788992 42887209984 1561504857088 62539090407424 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 17 304 9105 404736 24794905 1992310272 202567930817 25354445455360 3822552114728481 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A060187 | 1 1 -1 1 -6 1 1 -23 23 -1 1 -76 230 -76 1 1 -237 1682 -1682 237 -1 1 -722 10543 -23548 10543 -722 1 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A060187 | 1 -1 1 1 -6 1 -1 23 -23 1 1 -76 230 -76 1 -1 237 -1682 1682 -237 1 1 -722 10543 -23548 10543 -722 1 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -7 6 1 137 -115 -23 1 11945 -10044 -1978 76 1 -2588995 2177143 428418 -16330 -237 1 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 6 -7 1 -23 -115 137 1 76 -1978 -10044 11945 1 -237 -16330 428418 2177143 -2588995 1 722 |
| Alt | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A171273 | 1 1 1 5 6 1 93 115 23 1 5993 7436 1518 76 1 1272089 1578757 322762 16330 237 1 857402029 1064110290 |
| Alt | Accsee docs | missing | 1 1 0 1 -5 -4 1 -22 1 0 1 -75 155 79 80 1 -236 1446 -236 1 0 1 -721 9822 -13726 -3183 -3905 -3904 1 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -5 -4 -1 22 -1 0 1 -75 155 79 80 -1 236 -1446 236 -1 0 1 -721 9822 -13726 -3183 -3905 |
| Alt | AntiDiagsee docs | missing | 1 1 1 -1 1 -6 1 -23 1 1 -76 23 1 -237 230 -1 1 -722 1682 -76 1 -2179 10543 -1682 1 1 -6552 60657 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -12 3 1 -46 69 -4 1 -152 690 -304 5 1 -474 5046 -6728 1185 -6 1 -1444 31629 -94192 52715 |
| Alt | RowSum∑ k=0..n T(n, k) | A002436 | 1 0 -4 0 80 0 -3904 0 354560 0 -51733504 0 11070525440 0 -3266330312704 0 1270842139934720 0 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 2 24 232 1920 21088 322560 5338240 92897280 1832078848 40874803200 986530539520 25505877196800 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -6 -24 -152 -1920 -24992 -322560 -4983680 -92897280 -1883812352 -40874803200 -975460014080 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000165 | 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000165 | 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -5 -21 -52 -7 885 6684 30795 62759 -528984 -8154607 -65199719 -329601464 -183879397 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -8 -20 240 976 -15616 -88640 1772800 12933376 -310401024 -2767631360 77493678080 816582578176 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -8 20 240 -976 -15616 88640 1772800 -12933376 -310401024 2767631360 77493678080 -816582578176 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 6 23 8740 398634 89624229604 34328005245969 3371304106638422136 6508053348450890352622220 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | missing | 1 1 6 23 2 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A154420 | 1 1 6 23 230 1682 23548 259723 4675014 69413294 1527092468 28588019814 743288515164 16818059163492 |
| Alt | ColMiddleT(n, n // 2) | A154420 | 1 1 -6 -23 230 1682 -23548 -259723 4675014 69413294 -1527092468 -28588019814 743288515164 |
| Alt | CentralET(2 n, n) | A177043 | 1 -6 230 -23548 4675014 -1527092468 743288515164 -504541774904760 455522635895576646 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 -23 1682 -259723 69413294 -28588019814 16818059163492 -13397724585164019 13892023109165902550 |
| 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -10 0 774 0 -163332 0 67364166 0 -45892468524 0 46687337311900 0 -66323461965129160 0 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 14 -140 1990 -36012 795916 -20758712 624278342 -21265899980 809348930788 -34035791356008 |
| Alt | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 -4 20 160 -976 -11712 88640 1418240 -12933376 -258667520 2767631360 66423152640 -816582578176 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -8 20 240 -976 -15616 88640 1772800 -12933376 -310401024 2767631360 77493678080 -816582578176 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 -2 60 176 -4880 -19808 620480 3237376 -116400384 -743696896 30443944960 230372478976 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -7 -39 177 3441 -2007 -514359 -2913183 107756001 1777832793 -25512663879 -1062285896943 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A080253 | 1 -3 17 -147 1697 -24483 423857 -8560947 197613377 -5131725123 148070287697 -4699645934547 |
| Alt | DiagRow1T(n + 1, n) | A060188 | 1 -6 23 -76 237 -722 2179 -6552 19673 -59038 177135 -531428 1594309 -4782954 14348891 -43046704 |
| Alt | DiagRow2T(n + 2, n) | A060189 | 1 -23 230 -1682 10543 -60657 331612 -1756340 9116141 -46702427 237231970 -1198382694 6031771195 |
| Alt | DiagRow3T(n + 3, n) | A060190 | 1 -76 1682 -23548 259723 -2485288 21707972 -178300904 1403080725 -10708911188 79944249686 |
| Alt | DiagCol1T(n + 1, 1) | A060188 | -1 -6 -23 -76 -237 -722 -2179 -6552 -19673 -59038 -177135 -531428 -1594309 -4782954 -14348891 |
| Alt | DiagCol2T(n + 2, 2) | A060189 | 1 23 230 1682 10543 60657 331612 1756340 9116141 46702427 237231970 1198382694 6031771195 |
| Alt | DiagCol3T(n + 3, 3) | A060190 | -1 -76 -1682 -23548 -259723 -2485288 -21707972 -178300904 -1403080725 -10708911188 -79944249686 |
| Alt | Polysee docs | missing | 1 1 1 1 0 1 1 -4 -1 1 1 0 -7 -2 1 1 80 39 -8 -3 1 1 0 177 112 -7 -4 1 1 -3904 -3441 -128 213 -4 -5 |
| 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 | missing | 1 -4 -7 -8 -7 -4 1 8 17 28 41 56 73 92 113 136 161 188 217 248 281 316 353 392 433 476 521 568 617 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 0 39 112 213 336 475 624 777 928 1071 1200 1309 1392 1443 1456 1425 1344 1207 1008 741 400 -21 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -1 -7 39 177 -3441 -2007 514359 -2913183 -107756001 1777832793 25512663879 -1062285896943 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 -8 112 -128 -12032 136192 1411072 -61964288 297730048 27497070592 -669206970368 -8227911630848 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -7 112 -1231 -24384 3384961 -226461696 9665976897 323409295360 -167317061860279 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A171273 | 1 -1 1 5 -6 1 -93 115 -23 1 5993 -7436 1518 -76 1 -1272089 1578757 -322762 16330 -237 1 857402029 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -6 5 1 -23 115 -93 1 -76 1518 -7436 5993 1 -237 16330 -322762 1578757 -1272089 1 -722 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A060187 | 1 1 1 1 6 1 1 23 23 1 1 76 230 76 1 1 237 1682 1682 237 1 1 722 10543 23548 10543 722 1 1 2179 |
| Inv | Accsee docs | missing | 1 -1 0 5 -1 0 -93 22 -1 0 5993 -1443 75 -1 0 -1272089 306668 -16094 236 -1 0 857402029 -206708261 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -5 0 1 -22 93 0 1 -75 1443 -5993 0 1 -236 16094 -306668 1272089 0 1 -721 159850 -10852690 |
| Inv | AntiDiagsee docs | missing | 1 -1 5 1 -93 -6 5993 115 1 -1272089 -7436 -23 857402029 1578757 1518 1 -1792650585525 -1064110290 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 5 -12 3 -93 230 -69 4 5993 -14872 4554 -304 5 -1272089 3157514 -968286 65320 -1185 6 |
| Inv | RowSum∑ k=0..n T(n, k) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 6 -116 7512 -1595088 1075123552 -2247862240064 14375398946243968 -278882441653319691520 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -6 116 -7512 1595088 -1075123552 2247862240064 -14375398946243968 278882441653319691520 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 -2 12 -232 15024 -3190176 2150247104 -4495724480128 28750797892487936 -557764883306639383040 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 12 232 15024 3190176 2150247104 4495724480128 28750797892487936 557764883306639383040 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 6 -99 6109 -1279548 858982305 -1793715018653 11466480607396746 -222420548759232277467 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 4 -72 4624 -981280 661387328 -1382823986304 8843356107415808 -171560925204217369088 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -4 72 -4624 981280 -661387328 1382823986304 -8843356107415808 171560925204217369088 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 30 10695 4494102756 1254352845580753602413730 383972367241177062317562280537759735980 |
| Inv | 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 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 6 115 7436 1578757 1064110290 2224835452407 14228139328931096 276025608122908733321 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -6 115 1518 -322762 -11012540 23025275075 2147290464886 -41657391444153086 |
| Inv | CentralET(2 n, n) | missing | 1 -6 1518 -11012540 2147290464886 -10991486289326969076 1481130305191078491484585996 |
| Inv | CentralOT(2 n + 1, n) | missing | -1 115 -322762 23025275075 -41657391444153086 1938226040820344383545710 |
| Inv | ColLeftT(n, 0) | missing | 1 -1 5 -93 5993 -1272089 857402029 -1792650585525 11464255554367057 -222406320165016449457 |
| Inv | ColRightT(n, n) | A000012 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
| Inv | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -6 184 -14946 3556192 -2481692012 5022968503216 -29005196474209354 464916499650379529856 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 18 508 45150 12557980 10728141732 27736560614136 215138109927100854 4983508243569886816364 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 -4 72 -4624 981280 -661387328 1382823986304 -8843356107415808 171560925204217369088 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -4 72 -4624 981280 -661387328 1382823986304 -8843356107415808 171560925204217369088 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 -2 32 -2032 430912 -290428224 607224836096 -3883289161550592 75335729243645856768 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 9 -329 42321 -17963985 24215716313 -101260109984153 1295145618525878177 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 3 33 1251 161601 68614851 92494978401 386775868795299 4946973437912246913 |
| Inv | DiagRow1T(n + 1, n) | A060188 | -1 -6 -23 -76 -237 -722 -2179 -6552 -19673 -59038 -177135 -531428 -1594309 -4782954 -14348891 |
| Inv | DiagRow2T(n + 2, n) | missing | 5 115 1518 16330 160571 1512581 13945196 127141156 1152338433 10410993703 93897266810 846062060558 |
| Inv | DiagRow3T(n + 3, n) | missing | -93 -7436 -322762 -11012540 -335768223 -9673492136 -270538484020 -7446608913000 -203202094563809 |
| Inv | DiagCol1T(n + 1, 1) | missing | 1 -6 115 -7436 1578757 -1064110290 2224835452407 -14228139328931096 276025608122908733321 |
| Inv | DiagCol2T(n + 2, 2) | missing | 1 -23 1518 -322762 217560951 -454875884137 2908996087466828 -56434463826320585284 |
| Inv | DiagCol3T(n + 3, 3) | missing | 1 -76 16330 -11012540 23025275075 -147249943814184 2856645864675796564 -167312402773377971746920 |
| Inv | Polysee docs | missing | 1 -1 1 5 0 1 -93 0 1 1 5993 0 -3 2 1 -1272089 0 53 -4 3 1 857402029 0 -3399 72 -3 4 1 |
| 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 | missing | 5 0 -3 -4 -3 0 5 12 21 32 45 60 77 96 117 140 165 192 221 252 285 320 357 396 437 480 525 572 621 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -93 0 53 72 63 32 -15 -72 -133 -192 -243 -280 -297 -288 -247 -168 -45 128 357 648 1007 1440 1953 |
| Inv | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 1 -3 53 -3399 721257 -486128971 1016394955037 -6499990316797327 126099677431081309393 |
| Inv | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 -4 72 -4624 981280 -661387328 1382823986304 -8843356107415808 171560925204217369088 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -3 72 -4071 448896 128758285 -1391064478848 16904881967491217 -489248428395985776640 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | missing | 1 1 -1 1 -6 5 1 -23 115 -93 1 -76 1518 -7436 5993 1 -237 16330 -322762 1578757 -1272089 1 -722 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A171273 | 1 -1 1 5 -6 1 -93 115 -23 1 5993 -7436 1518 -76 1 -1272089 1578757 -322762 16330 -237 1 857402029 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A060187 | 1 1 1 1 6 1 1 23 23 1 1 76 230 76 1 1 237 1682 1682 237 1 1 722 10543 23548 10543 722 1 1 2179 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -5 0 1 -22 93 0 1 -75 1443 -5993 0 1 -236 16094 -306668 1272089 0 1 -721 159850 -10852690 |
| Inv:Rev | AccRevsee docs | missing | 1 -1 0 5 -1 0 -93 22 -1 0 5993 -1443 75 -1 0 -1272089 306668 -16094 236 -1 0 857402029 -206708261 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -6 1 -23 5 1 -76 115 1 -237 1518 -93 1 -722 16330 -7436 1 -2179 160571 -322762 5993 1 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -12 15 1 -46 345 -372 1 -152 4554 -29744 29965 1 -474 48990 -1291048 7893785 -7632534 1 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A000007 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 6 116 7512 1595088 1075123552 2247862240064 14375398946243968 278882441653319691520 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -6 -116 -7512 -1595088 -1075123552 -2247862240064 -14375398946243968 -278882441653319691520 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | missing | 1 2 12 232 15024 3190176 2150247104 4495724480128 28750797892487936 557764883306639383040 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | missing | 1 2 12 232 15024 3190176 2150247104 4495724480128 28750797892487936 557764883306639383040 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -5 -17 40 1189 8173 -158376 -7927753 -105553837 12414754768 1423885660057 35204301207977 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -4 72 -4624 981280 -661387328 1382823986304 -8843356107415808 171560925204217369088 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 4 -72 4624 -981280 661387328 -1382823986304 8843356107415808 -171560925204217369088 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 30 10695 4494102756 1254352845580753602413730 383972367241177062317562280537759735980 |
| Inv: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 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 6 115 7436 1578757 1064110290 2224835452407 14228139328931096 276025608122908733321 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -6 -23 1518 16330 -11012540 -335768223 2147290464886 187665608020478 -10991486289326969076 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 -6 1518 -11012540 2147290464886 -10991486289326969076 1481130305191078491484585996 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -23 16330 -335768223 187665608020478 -2794144125548953124662 1108172771490732215668663853876 |
| 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 5 -93 5993 -1272089 857402029 -1792650585525 11464255554367057 -222406320165016449457 |
| Inv:Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -6 184 -14946 3556192 -2481692012 5022968503216 -29005196474209354 464916499650379529856 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 18 -508 45150 -12557980 10728141732 -27736560614136 215138109927100854 -4983508243569886816364 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 4 -72 4624 -981280 661387328 -1382823986304 8843356107415808 -171560925204217369088 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 4 -72 4624 -981280 661387328 -1382823986304 8843356107415808 -171560925204217369088 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 14 -400 34960 -9381888 7646219712 -18752310972160 137610408557102336 -3012760924432266786816 |
| Inv:Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 1 -3 53 -3399 721257 -486128971 1016394955037 -6499990316797327 126099677431081309393 |
| Inv:Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | missing | 1 -3 21 -423 27561 -5855115 3946559037 -8251448061231 52769185205128017 -1023721099526827816467 |
| Inv:Rev | DiagRow1T(n + 1, n) | missing | 1 -6 115 -7436 1578757 -1064110290 2224835452407 -14228139328931096 276025608122908733321 |
| Inv:Rev | DiagRow2T(n + 2, n) | missing | 1 -23 1518 -322762 217560951 -454875884137 2908996087466828 -56434463826320585284 |
| Inv:Rev | DiagRow3T(n + 3, n) | missing | 1 -76 16330 -11012540 23025275075 -147249943814184 2856645864675796564 -167312402773377971746920 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A060188 | -1 -6 -23 -76 -237 -722 -2179 -6552 -19673 -59038 -177135 -531428 -1594309 -4782954 -14348891 |
| Inv:Rev | DiagCol2T(n + 2, 2) | missing | 5 115 1518 16330 160571 1512581 13945196 127141156 1152338433 10410993703 93897266810 846062060558 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | -93 -7436 -322762 -11012540 -335768223 -9673492136 -270538484020 -7446608913000 -203202094563809 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 0 -1 1 1 0 9 -2 1 1 0 -329 28 -3 1 1 0 42321 -1544 57 -4 1 1 0 -17963985 298096 -4203 |
| 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 | A135705 | 1 0 9 28 57 96 145 204 273 352 441 540 649 768 897 1036 1185 1344 1513 1692 1881 2080 2289 2508 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 0 -329 -1544 -4203 -8864 -16085 -26424 -40439 -58688 -81729 -110120 -144419 -185184 -232973 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -1 9 -329 42321 -17963985 24215716313 -101260109984153 1295145618525878177 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 28 -1544 298096 -189806624 383793820096 -2407300630438016 46185090060715280128 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 9 -1544 1082289 -3028493184 32008013510065 -1222165105408418688 163257480439413162352193 |
| << | 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.