OEIS Similars: A028338, A039757, A039758, A109692
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A028338 | 1 1 1 3 4 1 15 23 9 1 105 176 86 16 1 945 1689 950 230 25 1 10395 19524 12139 3480 505 36 1 135135 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A109692 | 1 1 1 1 4 3 1 9 23 15 1 16 86 176 105 1 25 230 950 1689 945 1 36 505 3480 12139 19524 10395 1 49 |
| Std | InvT-1(n, k), 0 ≤ k ≤ n | A039755 | 1 -1 1 1 -4 1 -1 13 -9 1 1 -40 58 -16 1 -1 121 -330 170 -25 1 1 -364 1771 -1520 395 -36 1 -1 1093 |
| Std | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A039756 | 1 1 -1 1 -4 1 1 -9 13 -1 1 -16 58 -40 1 1 -25 170 -330 121 -1 1 -36 395 -1520 1771 -364 1 1 -49 791 |
| Std | Accsee docs | missing | 1 1 2 3 7 8 15 38 47 48 105 281 367 383 384 945 2634 3584 3814 3839 3840 10395 29919 42058 45538 |
| Std | AccRevsee docs | missing | 1 1 2 1 5 8 1 10 33 48 1 17 103 279 384 1 26 256 1206 2895 3840 1 37 542 4022 16161 35685 46080 1 |
| Std | AntiDiagsee docs | missing | 1 1 3 1 15 4 105 23 1 945 176 9 10395 1689 86 1 135135 19524 950 16 2027025 264207 12139 230 1 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 3 8 3 15 46 27 4 105 352 258 64 5 945 3378 2850 920 125 6 10395 39048 36417 13920 2525 216 7 |
| 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) | A002866 | 1 1 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A002866 | 0 1 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 |
| Std | AltSum∑ k=0..n T(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 | 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) | missing | 1 1 4 19 129 1130 12171 155625 2303602 38738501 729408237 15200872256 347334515813 8634091342069 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 18 148 1520 18656 266112 4324608 78870528 1595142144 35432939520 857558384640 22461642178560 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 14 92 784 8224 102528 1481472 24348672 448598016 9157754880 205186498560 5006225571840 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 12 1035 794640 2324992950 4810656157072920 182911242997871793405 409032268138980471585600 |
| 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) | | A004041 | 1 1 4 23 176 1689 19524 264207 4098240 71697105 1396704420 29985521895 703416314160 17901641997225 |
| Std | ColMiddleT(n, n // 2) | missing | 1 1 4 23 86 950 3480 57379 208054 4574934 16486680 453714470 1628301884 53845005500 192666441968 |
| Std | CentralET(2 n, n) | A293318 | 1 4 86 3480 208054 16486680 1628301884 192666441968 26569595376038 4184718381424152 |
| Std | CentralOT(2 n + 1, n) | missing | 1 23 950 57379 4574934 453714470 53845005500 7442156684963 1174199725349222 208251057899323218 |
| Std | ColLeftT(n, 0) | A001147 | 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| 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 12 112 1390 21316 387016 8089152 190810614 5004826108 144299948936 4531481715168 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -4 28 -146 176 13096 -332856 6220278 -100254944 1315515816 -7548862936 -376130570804 |
| Std | TransNat0∑ k=0..n T(n, k) k | A203159 | 0 1 6 44 400 4384 56448 836352 14026752 262803456 5441863680 123436892160 3044235018240 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 14 92 784 8224 102528 1481472 24348672 448598016 9157754880 205186498560 5006225571840 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 8 68 680 7984 108416 1676800 29146624 563014656 11971694592 277976899584 7000068980736 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A008545 | 1 3 21 231 3465 65835 1514205 40883535 1267389585 44358635475 1729986783525 74389431691575 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A007696 | 1 -1 5 -45 585 -9945 208845 -5221125 151412625 -4996616625 184874815125 -7579867420125 |
| Std | DiagRow1T(n + 1, n) | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Std | DiagRow2T(n + 2, n) | A024196 | 3 23 86 230 505 973 1708 2796 4335 6435 9218 12818 17381 23065 30040 38488 48603 60591 74670 91070 |
| Std | DiagRow3T(n + 3, n) | A024197 | 15 176 950 3480 10045 24640 53676 106800 197835 345840 576290 922376 1426425 2141440 3132760 |
| Std | DiagCol1T(n + 1, 1) | A004041 | 1 4 23 176 1689 19524 264207 4098240 71697105 1396704420 29985521895 703416314160 17901641997225 |
| Std | DiagCol2T(n + 2, 2) | A028339 | 1 9 86 950 12139 177331 2924172 53809164 1094071221 24372200061 590546123298 15467069396610 |
| Std | DiagCol3T(n + 3, 3) | A028340 | 1 16 230 3480 57379 1038016 20570444 444647600 10431670821 264300628944 7198061846898 |
| Std | Polysee docs | missing | 1 1 1 3 2 1 15 8 3 1 105 48 15 4 1 945 384 105 24 5 1 10395 3840 945 192 35 6 1 135135 46080 10395 |
| 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 | A005563 | 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728 783 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A370912 | 15 48 105 192 315 480 693 960 1287 1680 2145 2688 3315 4032 4845 5760 6783 7920 9177 10560 12075 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A001147 | 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A002866 | 1 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A374866 | 1 2 15 192 3465 80640 2297295 77414400 3011753745 132843110400 6550564395375 357082280755200 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A028338 | 1 1 -1 3 -4 1 15 -23 9 -1 105 -176 86 -16 1 945 -1689 950 -230 25 -1 10395 -19524 12139 -3480 505 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A109692 | 1 -1 1 1 -4 3 -1 9 -23 15 1 -16 86 -176 105 -1 25 -230 950 -1689 945 1 -36 505 -3480 12139 -19524 |
| Alt | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -7 4 1 25 -13 -9 1 721 -376 -230 16 1 -8259 4299 2730 -170 -25 1 -519375 270372 170971 |
| Alt | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 4 -7 1 -9 -13 25 1 16 -230 -376 721 1 -25 -170 2730 4299 -8259 1 36 -1405 -10720 170971 |
| Alt | Accsee docs | missing | 1 1 0 3 -1 0 15 -8 1 0 105 -71 15 -1 0 945 -744 206 -24 1 0 10395 -9129 3010 -470 35 -1 0 135135 |
| Alt | AccRevsee docs | missing | 1 -1 0 1 -3 0 -1 8 -15 0 1 -15 71 -105 0 -1 24 -206 744 -945 0 1 -35 470 -3010 9129 -10395 0 -1 48 |
| Alt | AntiDiagsee docs | missing | 1 1 3 -1 15 -4 105 -23 1 945 -176 9 10395 -1689 86 -1 135135 -19524 950 -16 2027025 -264207 12139 |
| Alt | Diffx1T(n, k) (k+1) | missing | 1 1 -2 3 -8 3 15 -46 27 -4 105 -352 258 -64 5 945 -3378 2850 -920 125 -6 10395 -39048 36417 -13920 |
| Alt | 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 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A002866 | 1 1 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A002866 | 0 -1 -4 -24 -192 -1920 -23040 -322560 -5160960 -92897280 -1857945600 -40874803200 -980995276800 |
| 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 2 11 83 778 8791 116545 1774728 30535061 585899267 12405387312 287322329189 7226369369269 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A000165 | 1 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Alt | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A000165 | 1 -1 -2 -8 -48 -384 -3840 -46080 -645120 -10321920 -185794560 -3715891200 -81749606400 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 12 1035 794640 2324992950 4810656157072920 182911242997871793405 409032268138980471585600 |
| 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) | | A004041 | 1 1 4 23 176 1689 19524 264207 4098240 71697105 1396704420 29985521895 703416314160 17901641997225 |
| Alt | ColMiddleT(n, n // 2) | missing | 1 1 -4 -23 86 950 -3480 -57379 208054 4574934 -16486680 -453714470 1628301884 53845005500 |
| Alt | CentralET(2 n, n) | A293318 | 1 -4 86 -3480 208054 -16486680 1628301884 -192666441968 26569595376038 -4184718381424152 |
| Alt | CentralOT(2 n + 1, n) | missing | 1 -23 950 -57379 4574934 -453714470 53845005500 -7442156684963 1174199725349222 -208251057899323218 |
| Alt | ColLeftT(n, 0) | A001147 | 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -4 -28 -146 -176 13096 332856 6220278 100254944 1315515816 7548862936 -376130570804 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 12 -112 1390 -21316 387016 -8089152 190810614 -5004826108 144299948936 -4531481715168 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A000165 | 0 -1 -2 -8 -48 -384 -3840 -46080 -645120 -10321920 -185794560 -3715891200 -81749606400 |
| Alt | TransNat1∑ k=0..n T(n, k) (k + 1) | A000165 | 1 -1 -2 -8 -48 -384 -3840 -46080 -645120 -10321920 -185794560 -3715891200 -81749606400 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 0 4 40 416 4928 66816 1027584 17731584 339812352 7167836160 165124177920 4126479482880 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A007696 | 1 1 5 45 585 9945 208845 5221125 151412625 4996616625 184874815125 7579867420125 341094033905625 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A008545 | 1 -3 21 -231 3465 -65835 1514205 -40883535 1267389585 -44358635475 1729986783525 -74389431691575 |
| Alt | DiagRow1T(n + 1, n) | A000290 | 1 -4 9 -16 25 -36 49 -64 81 -100 121 -144 169 -196 225 -256 289 -324 361 -400 441 -484 529 -576 625 |
| Alt | DiagRow2T(n + 2, n) | A024196 | 3 -23 86 -230 505 -973 1708 -2796 4335 -6435 9218 -12818 17381 -23065 30040 -38488 48603 -60591 |
| Alt | DiagRow3T(n + 3, n) | A024197 | 15 -176 950 -3480 10045 -24640 53676 -106800 197835 -345840 576290 -922376 1426425 -2141440 3132760 |
| Alt | DiagCol1T(n + 1, 1) | A004041 | -1 -4 -23 -176 -1689 -19524 -264207 -4098240 -71697105 -1396704420 -29985521895 -703416314160 |
| Alt | DiagCol2T(n + 2, 2) | A028339 | 1 9 86 950 12139 177331 2924172 53809164 1094071221 24372200061 590546123298 15467069396610 |
| Alt | DiagCol3T(n + 3, 3) | A028340 | -1 -16 -230 -3480 -57379 -1038016 -20570444 -444647600 -10431670821 -264300628944 -7198061846898 |
| Alt | Polysee docs | missing | 1 1 1 3 0 1 15 0 -1 1 105 0 -1 -2 1 945 0 -3 0 -3 1 10395 0 -15 0 3 -4 1 135135 0 -105 0 3 8 -5 1 |
| 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 | A005563 | 3 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 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 15 0 -3 0 3 0 -15 -48 -105 -192 -315 -480 -693 -960 -1287 -1680 -2145 -2688 -3315 -4032 -4845 -5760 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A001147 | 1 -1 -1 -3 -15 -105 -945 -10395 -135135 -2027025 -34459425 -654729075 -13749310575 -316234143225 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | 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 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | A177145 | 1 0 -1 0 9 0 -225 0 11025 0 -893025 0 108056025 0 -18261468225 0 4108830350625 0 -1187451971330625 |
| Rev | TriangleT(n, k), 0 ≤ k ≤ n | A109692 | 1 1 1 1 4 3 1 9 23 15 1 16 86 176 105 1 25 230 950 1689 945 1 36 505 3480 12139 19524 10395 1 49 |
| Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A039755 | 1 -1 1 1 -4 1 -1 13 -9 1 1 -40 58 -16 1 -1 121 -330 170 -25 1 1 -364 1771 -1520 395 -36 1 -1 1093 |
| Rev | Accsee docs | missing | 1 1 2 1 5 8 1 10 33 48 1 17 103 279 384 1 26 256 1206 2895 3840 1 37 542 4022 16161 35685 46080 1 |
| Rev | AccRevsee docs | missing | 1 1 2 3 7 8 15 38 47 48 105 281 367 383 384 945 2634 3584 3814 3839 3840 10395 29919 42058 45538 |
| Rev | AntiDiagsee docs | missing | 1 1 1 1 1 4 1 9 3 1 16 23 1 25 86 15 1 36 230 176 1 49 505 950 105 1 64 973 3480 1689 1 81 1708 |
| Rev | Diffx1T(n, k) (k+1) | missing | 1 1 2 1 8 9 1 18 69 60 1 32 258 704 525 1 50 690 3800 8445 5670 1 72 1515 13920 60695 117144 72765 |
| Rev | RowSum∑ k=0..n T(n, k) | A000165 | 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Rev | EvenSum∑ k=0..n T(n, k) even(k) | A002866 | 1 1 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 |
| Rev | OddSum∑ k=0..n T(n, k) odd(k) | A002866 | 0 1 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 |
| Rev | AltSum∑ k=0..n T(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 | AbsSum∑ k=0..n | T(n, k) | | A000165 | 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | A202153 | 1 1 2 5 13 40 127 443 1610 6207 24919 104440 453913 2042537 9488242 45403797 223433077 1128619968 |
| Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 3 14 92 784 8224 102528 1481472 24348672 448598016 9157754880 205186498560 5006225571840 |
| Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 3 18 148 1520 18656 266112 4324608 78870528 1595142144 35432939520 857558384640 22461642178560 |
| Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 12 1035 794640 2324992950 4810656157072920 182911242997871793405 409032268138980471585600 |
| 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) | | A004041 | 1 1 4 23 176 1689 19524 264207 4098240 71697105 1396704420 29985521895 703416314160 17901641997225 |
| Rev | ColMiddleT(n, n // 2) | missing | 1 1 4 9 86 230 3480 10045 208054 626934 16486680 51069018 1628301884 5141534684 192666441968 |
| Rev | CentralET(2 n, n) | A293318 | 1 4 86 3480 208054 16486680 1628301884 192666441968 26569595376038 4184718381424152 |
| Rev | CentralOT(2 n + 1, n) | missing | 1 9 230 10045 626934 51069018 5141534684 617014151325 86014818744998 13663776163658478 |
| 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) | A001147 | 1 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Rev | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 2 12 112 1390 21316 387016 8089152 190810614 5004826108 144299948936 4531481715168 |
| Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 0 -4 -28 -146 -176 13096 332856 6220278 100254944 1315515816 7548862936 -376130570804 |
| Rev | TransNat0∑ k=0..n T(n, k) k | A197130 | 0 1 10 100 1136 14816 220032 3679488 68548608 1409347584 31717048320 775808778240 20499651624960 |
| Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 3 18 148 1520 18656 266112 4324608 78870528 1595142144 35432939520 857558384640 22461642178560 |
| Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 16 236 3624 60144 1089920 21578752 465321472 10881911808 274723540992 7454067646464 |
| Rev | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A001147 | 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625 |
| Rev | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A001147 | 1 -1 -1 -3 -15 -105 -945 -10395 -135135 -2027025 -34459425 -654729075 -13749310575 -316234143225 |
| Rev | DiagRow1T(n + 1, n) | A004041 | 1 4 23 176 1689 19524 264207 4098240 71697105 1396704420 29985521895 703416314160 17901641997225 |
| Rev | DiagRow2T(n + 2, n) | A028339 | 1 9 86 950 12139 177331 2924172 53809164 1094071221 24372200061 590546123298 15467069396610 |
| Rev | DiagRow3T(n + 3, n) | A028340 | 1 16 230 3480 57379 1038016 20570444 444647600 10431670821 264300628944 7198061846898 |
| Rev | DiagCol1T(n + 1, 1) | A000290 | 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484 529 576 625 676 729 784 |
| Rev | DiagCol2T(n + 2, 2) | A024196 | 3 23 86 230 505 973 1708 2796 4335 6435 9218 12818 17381 23065 30040 38488 48603 60591 74670 91070 |
| Rev | DiagCol3T(n + 3, 3) | A024197 | 15 176 950 3480 10045 24640 53676 106800 197835 345840 576290 922376 1426425 2141440 3132760 |
| Rev | Polysee docs | missing | 1 1 1 1 2 1 1 8 3 1 1 48 21 4 1 1 384 231 40 5 1 1 3840 3465 640 65 6 1 1 46080 65835 14080 1365 96 |
| 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 | A000567 | 1 8 21 40 65 96 133 176 225 280 341 408 481 560 645 736 833 936 1045 1160 1281 1408 1541 1680 1825 |
| Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 48 231 640 1365 2496 4123 6336 9225 12880 17391 22848 29341 36960 45795 55936 67473 80496 95095 |
| Rev | PolyCol2∑ k=0..n T(n, k) 2^k | A008545 | 1 3 21 231 3465 65835 1514205 40883535 1267389585 44358635475 1729986783525 74389431691575 |
| Rev | PolyCol3∑ k=0..n T(n, k) 3^k | A049308 | 1 4 40 640 14080 394240 13404160 536166400 24663654400 1282510028800 74385581670400 |
| Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 2 21 640 39585 4133376 653309965 145494835200 43403901242625 16705186398208000 |
| Inv | TriangleT(n, k), 0 ≤ k ≤ n | A039755 | 1 -1 1 1 -4 1 -1 13 -9 1 1 -40 58 -16 1 -1 121 -330 170 -25 1 1 -364 1771 -1520 395 -36 1 -1 1093 |
| Inv | RevT(n, n - k), 0 ≤ k ≤ n | A039756 | 1 1 -1 1 -4 1 1 -9 13 -1 1 -16 58 -40 1 1 -25 170 -330 121 -1 1 -36 395 -1520 1771 -364 1 1 -49 791 |
| Inv | RevInvT-1(n, n - k), 0 ≤ k ≤ n | A109692 | 1 1 1 1 4 3 1 9 23 15 1 16 86 176 105 1 25 230 950 1689 945 1 36 505 3480 12139 19524 10395 1 49 |
| Inv | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | missing | 1 -1 1 -5 4 1 55 -43 -13 1 2473 -1936 -578 40 1 -280259 219411 65478 -4510 -121 1 -106308421 |
| Inv | Accsee docs | missing | 1 -1 0 1 -3 -2 -1 12 3 4 1 -39 19 3 4 -1 120 -210 -40 -65 -64 1 -363 1408 -112 283 247 248 -1 1092 |
| Inv | AccRevsee docs | missing | 1 1 0 1 -3 -2 1 -8 5 4 1 -15 43 3 4 1 -24 146 -184 -63 -64 1 -35 360 -1160 611 247 248 1 -48 743 |
| Inv | AntiDiagsee docs | missing | 1 -1 1 1 -1 -4 1 13 1 -1 -40 -9 1 121 58 1 -1 -364 -330 -16 1 1093 1771 170 1 -1 -3280 -9219 -1520 |
| Inv | Diffx1T(n, k) (k+1) | missing | 1 -1 2 1 -8 3 -1 26 -27 4 1 -80 174 -64 5 -1 242 -990 680 -125 6 1 -728 5313 -6080 1975 -216 7 -1 |
| Inv | RowSum∑ k=0..n T(n, k) | A334190 | 1 0 -2 4 4 -64 248 -48 -6512 51200 -171296 -830400 17870400 -144684032 441316224 5976726784 |
| Inv | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 -1 2 -10 60 -356 2168 -14344 106704 -890512 8129440 -79192224 812374720 -8747469888 98997480832 |
| Inv | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 1 -4 14 -56 292 -1920 14296 -113216 941712 -8300736 78361824 -794504320 8602785856 -98556164608 |
| Inv | AltSum∑ k=0..n T(n, k) (-1)^k | A007405 | 1 -2 6 -24 116 -648 4088 -28640 219920 -1832224 16430176 -157554048 1606879040 -17350255744 |
| Inv | AbsSum∑ k=0..n | T(n, k) | | A007405 | 1 2 6 24 116 648 4088 28640 219920 1832224 16430176 157554048 1606879040 17350255744 197553645440 |
| Inv | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 -1 2 -5 15 -50 181 -711 3036 -14045 69837 -369952 2073253 -12235885 75836242 -492557937 |
| Inv | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 -1 -4 18 -12 -260 1712 -3640 -33008 426352 -2299456 -1029600 159973184 -1804918336 9608106752 |
| Inv | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 1 -4 2 36 -188 272 3208 -32112 136848 243904 -9765600 90212416 -365342144 -2547047168 65916404864 |
| Inv | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 117 2320 308550 24881416560 3415119838107075 10927777609869120 8184449743464324553963740 |
| Inv | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 1 4 1 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 |
| Inv | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 13 58 330 1771 12411 96096 719860 6289690 61885450 595122671 5929706783 70856013228 |
| Inv | ColMiddleT(n, n // 2) | missing | 1 -1 -4 13 58 -330 -1520 12411 58086 -618870 -2924712 38461522 182959876 -2863440580 -13685763520 |
| Inv | CentralET(2 n, n) | missing | 1 -4 58 -1520 58086 -2924712 182959876 -13685763520 1191663940038 -118406147270840 |
| Inv | CentralOT(2 n + 1, n) | A348087 | -1 13 -330 12411 -618870 38461522 -2863440580 248440887123 -24616763946918 2742625188929990 |
| 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 12 126 -1120 -308 87080 -752314 -2251680 128688828 -1301351480 -5093196628 349093094272 |
| Inv | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 2 10 68 574 5732 65292 830216 11606854 176361980 2886472156 50523676216 940246612268 |
| Inv | TransNat0∑ k=0..n T(n, k) k | missing | 0 1 -2 -2 32 -124 24 3256 -25600 85648 415200 -8935200 72342016 -220658112 -2988363392 59939678080 |
| Inv | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 1 -4 2 36 -188 272 3208 -32112 136848 243904 -9765600 90212416 -365342144 -2547047168 65916404864 |
| Inv | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 0 -14 64 -44 -1504 12776 -46080 -182000 4381952 -36586208 119264256 1421839680 -29749180928 |
| Inv | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | missing | 1 -1 -3 27 -103 -105 6101 -64141 350129 1270447 -63509459 965614155 -8377825207 -7124350649 |
| Inv | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A355165 | 1 3 13 79 601 5339 53861 607527 7560625 102637235 1506225085 23726435583 398852249097 7120170905995 |
| Inv | DiagRow1T(n + 1, n) | A000290 | -1 -4 -9 -16 -25 -36 -49 -64 -81 -100 -121 -144 -169 -196 -225 -256 -289 -324 -361 -400 -441 -484 |
| Inv | DiagRow2T(n + 2, n) | A103220 | 1 13 58 170 395 791 1428 2388 3765 5665 8206 11518 15743 21035 27560 35496 45033 56373 69730 85330 |
| Inv | DiagRow3T(n + 3, n) | missing | -1 -40 -330 -1520 -5075 -13776 -32340 -68160 -132165 -239800 -412126 -677040 -1070615 -1638560 |
| Inv | DiagCol1T(n + 1, 1) | A003462 | 1 -4 13 -40 121 -364 1093 -3280 9841 -29524 88573 -265720 797161 -2391484 7174453 -21523360 |
| Inv | DiagCol2T(n + 2, 2) | A016209 | 1 -9 58 -330 1771 -9219 47188 -239220 1205941 -6059229 30384718 -152189310 761743711 -3811110039 |
| Inv | DiagCol3T(n + 3, 3) | A021424 | 1 -16 170 -1520 12411 -96096 719860 -5278240 38153621 -273134576 1942326750 -13748476560 |
| Inv | Polysee docs | missing | 1 -1 1 1 0 1 -1 -2 1 1 1 4 -3 2 1 -1 4 -3 -2 3 1 1 -64 41 -16 1 4 1 -1 248 -87 52 -29 6 5 1 1 -48 |
| 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 | A123968 | 1 -2 -3 -2 1 6 13 22 33 46 61 78 97 118 141 166 193 222 253 286 321 358 397 438 481 526 573 622 673 |
| Inv | PolyRow3∑ k=0..3 T(3, k) n^k | missing | -1 4 -3 -16 -29 -36 -31 -8 39 116 229 384 587 844 1161 1544 1999 2532 3149 3856 4659 5564 6577 7704 |
| Inv | 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 | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 2 -2 -16 52 200 -2216 3008 85264 -742624 39904 57578240 -559969472 54927488 63964454272 |
| Inv | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -3 -16 1 1104 11893 -19104 -2797951 -41382784 209758861 22229683200 390747598657 -4304791023872 |
| Inv:Rev | TriangleT(n, k), 0 ≤ k ≤ n | A039756 | 1 1 -1 1 -4 1 1 -9 13 -1 1 -16 58 -40 1 1 -25 170 -330 121 -1 1 -36 395 -1520 1771 -364 1 1 -49 791 |
| Inv:Rev | RevT(n, n - k), 0 ≤ k ≤ n | A039755 | 1 -1 1 1 -4 1 -1 13 -9 1 1 -40 58 -16 1 -1 121 -330 170 -25 1 1 -364 1771 -1520 395 -36 1 -1 1093 |
| Inv:Rev | InvT-1(n, k), 0 ≤ k ≤ n | missing | 1 -1 1 -5 4 1 55 -43 -13 1 2473 -1936 -578 40 1 -280259 219411 65478 -4510 -121 1 -106308421 |
| Inv:Rev | RevInvT-1(n, n - k), 0 ≤ k ≤ n | missing | 1 1 -1 1 4 -5 1 -13 -43 55 1 40 -578 -1936 2473 1 -121 -4510 65478 219411 -280259 1 364 -45815 |
| Inv:Rev | InvRev(T(n, n - k))-1, 0 ≤ k ≤ n | A028338 | 1 1 1 3 4 1 15 23 9 1 105 176 86 16 1 945 1689 950 230 25 1 10395 19524 12139 3480 505 36 1 135135 |
| Inv:Rev | Accsee docs | missing | 1 1 0 1 -3 -2 1 -8 5 4 1 -15 43 3 4 1 -24 146 -184 -63 -64 1 -35 360 -1160 611 247 248 1 -48 743 |
| Inv:Rev | AccRevsee docs | missing | 1 -1 0 1 -3 -2 -1 12 3 4 1 -39 19 3 4 -1 120 -210 -40 -65 -64 1 -363 1408 -112 283 247 248 -1 1092 |
| Inv:Rev | AntiDiagsee docs | missing | 1 1 1 -1 1 -4 1 -9 1 1 -16 13 1 -25 58 -1 1 -36 170 -40 1 -49 395 -330 1 1 -64 791 -1520 121 1 -81 |
| Inv:Rev | Diffx1T(n, k) (k+1) | missing | 1 1 -2 1 -8 3 1 -18 39 -4 1 -32 174 -160 5 1 -50 510 -1320 605 -6 1 -72 1185 -6080 8855 -2184 7 1 |
| Inv:Rev | RowSum∑ k=0..n T(n, k) | A334190 | 1 0 -2 4 4 -64 248 -48 -6512 51200 -171296 -830400 17870400 -144684032 441316224 5976726784 |
| Inv:Rev | EvenSum∑ k=0..n T(n, k) even(k) | missing | 1 1 2 14 60 292 2168 14296 106704 941712 8129440 78361824 812374720 8602785856 98997480832 |
| Inv:Rev | OddSum∑ k=0..n T(n, k) odd(k) | missing | 0 -1 -4 -10 -56 -356 -1920 -14344 -113216 -890512 -8300736 -79192224 -794504320 -8747469888 |
| Inv:Rev | AltSum∑ k=0..n T(n, k) (-1)^k | A007405 | 1 2 6 24 116 648 4088 28640 219920 1832224 16430176 157554048 1606879040 17350255744 197553645440 |
| Inv:Rev | AbsSum∑ k=0..n | T(n, k) | | A007405 | 1 2 6 24 116 648 4088 28640 219920 1832224 16430176 157554048 1606879040 17350255744 197553645440 |
| Inv:Rev | DiagSum∑ k=0..n // 2 T(n - k, k) | missing | 1 1 0 -3 -7 -2 33 95 18 -671 -1957 560 20173 51981 -65768 -784167 -1562147 5090422 36158029 |
| Inv:Rev | AccSum∑ k=0..n ∑ j=0..k T(n, j) | missing | 1 1 -4 2 36 -188 272 3208 -32112 136848 243904 -9765600 90212416 -365342144 -2547047168 65916404864 |
| Inv:Rev | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | missing | 1 -1 -4 18 -12 -260 1712 -3640 -33008 426352 -2299456 -1029600 159973184 -1804918336 9608106752 |
| Inv:Rev | RowLcmLcm k=0..n | T(n, k) | > 1 | missing | 1 1 4 117 2320 308550 24881416560 3415119838107075 10927777609869120 8184449743464324553963740 |
| Inv:Rev | RowGcdGcd k=0..n | T(n, k) | > 1 | A297382 | 1 1 4 1 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 |
| Inv:Rev | RowMaxMax k=0..n | T(n, k) | | missing | 1 1 4 13 58 330 1771 12411 96096 719860 6289690 61885450 595122671 5929706783 70856013228 |
| Inv:Rev | ColMiddleT(n, n // 2) | missing | 1 1 -4 -9 58 170 -1520 -5075 58086 209622 -2924712 -11115258 182959876 721488196 -13685763520 |
| Inv:Rev | CentralET(2 n, n) | missing | 1 -4 58 -1520 58086 -2924712 182959876 -13685763520 1191663940038 -118406147270840 |
| Inv:Rev | CentralOT(2 n + 1, n) | missing | 1 -9 170 -5075 209622 -11115258 721488196 -55483708995 4936283332838 -498999482959406 |
| 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 | BinConv∑ k=0..n C(n, k) T(n, k) | missing | 1 0 -6 12 126 -1120 -308 87080 -752314 -2251680 128688828 -1301351480 -5093196628 349093094272 |
| Inv:Rev | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | missing | 1 -2 10 -68 574 -5732 65292 -830216 11606854 -176361980 2886472156 -50523676216 940246612268 |
| Inv:Rev | TransNat0∑ k=0..n T(n, k) k | missing | 0 -1 -2 14 -16 -196 1464 -3592 -26496 375152 -2128160 -199200 142102784 -1660234304 9166790528 |
| Inv:Rev | TransNat1∑ k=0..n T(n, k) (k + 1) | missing | 1 -1 -4 18 -12 -260 1712 -3640 -33008 426352 -2299456 -1029600 159973184 -1804918336 9608106752 |
| Inv:Rev | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 0 34 -128 -404 7136 -35160 -53248 2423536 -21051648 59509792 956393472 -17292650816 |
| Inv:Rev | 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:Rev | 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 |
| Inv:Rev | DiagRow1T(n + 1, n) | A003462 | 1 -4 13 -40 121 -364 1093 -3280 9841 -29524 88573 -265720 797161 -2391484 7174453 -21523360 |
| Inv:Rev | DiagRow2T(n + 2, n) | A016209 | 1 -9 58 -330 1771 -9219 47188 -239220 1205941 -6059229 30384718 -152189310 761743711 -3811110039 |
| Inv:Rev | DiagRow3T(n + 3, n) | A021424 | 1 -16 170 -1520 12411 -96096 719860 -5278240 38153621 -273134576 1942326750 -13748476560 |
| Inv:Rev | DiagCol1T(n + 1, 1) | A000290 | -1 -4 -9 -16 -25 -36 -49 -64 -81 -100 -121 -144 -169 -196 -225 -256 -289 -324 -361 -400 -441 -484 |
| Inv:Rev | DiagCol2T(n + 2, 2) | A103220 | 1 13 58 170 395 791 1428 2388 3765 5665 8206 11518 15743 21035 27560 35496 45033 56373 69730 85330 |
| Inv:Rev | DiagCol3T(n + 3, 3) | missing | -1 -40 -330 -1520 -5075 -13776 -32340 -68160 -132165 -239800 -412126 -677040 -1070615 -1638560 |
| Inv:Rev | Polysee docs | missing | 1 1 1 1 0 1 1 -2 -1 1 1 4 -3 -2 1 1 4 27 -2 -3 1 1 -64 -103 64 1 -4 1 1 248 -105 -524 109 6 -5 1 1 |
| 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 | A123968 | 1 -2 -3 -2 1 6 13 22 33 46 61 78 97 118 141 166 193 222 253 286 321 358 397 438 481 526 573 622 673 |
| Inv:Rev | PolyRow3∑ k=0..3 T(3, k) n^k | missing | 1 4 27 64 109 156 199 232 249 244 211 144 37 -116 -321 -584 -911 -1308 -1781 -2336 -2979 -3716 |
| Inv:Rev | PolyCol2∑ k=0..n T(n, k) 2^k | missing | 1 -1 -3 27 -103 -105 6101 -64141 350129 1270447 -63509459 965614155 -8377825207 -7124350649 |
| Inv:Rev | PolyCol3∑ k=0..n T(n, k) 3^k | missing | 1 -2 -2 64 -524 2104 18136 -570368 8227600 -68107040 -288688160 26416365568 -660041056448 |
| Inv:Rev | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 -3 64 -1439 35376 -802907 919584 2590253825 -373575072896 44301151435501 -4951308848044800 |
| << | 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.