CATALAN[0] 1
[1] 0, 1
[2] 0, 2, 1
[3] 0, 5, 4, 1
[4] 0, 14, 14, 6, 1
[5] 0, 42, 48, 27, 8, 1

      OEIS Similars: A128899, A039598

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA1288991 0 1 0 2 1 0 5 4 1 0 14 14 6 1 0 42 48 27 8 1 0 132 165 110 44 10 1 0 429 572 429 208 65 12 1 0
StdRevT(n, n - k), 0 ≤ k ≤ nmissing1 1 0 1 2 0 1 4 5 0 1 6 14 14 0 1 8 27 48 42 0 1 10 44 110 165 132 0 1 12 65 208 429 572 429 0 1 14
StdInvT-1(n, k), 0 ≤ k ≤ nA1289081 0 1 0 -2 1 0 3 -4 1 0 -4 10 -6 1 0 5 -20 21 -8 1 0 -6 35 -56 36 -10 1 0 7 -56 126 -120 55 -12 1 0
StdRevInvT-1(n, n - k), 0 ≤ k ≤ nmissing1 1 0 1 -2 0 1 -4 3 0 1 -6 10 -4 0 1 -8 21 -20 5 0 1 -10 36 -56 35 -6 0 1 -12 55 -120 126 -56 7 0 1
StdAccsee docsmissing1 0 1 0 2 3 0 5 9 10 0 14 28 34 35 0 42 90 117 125 126 0 132 297 407 451 461 462 0 429 1001 1430
StdAccRevsee docsmissing1 1 1 1 3 3 1 5 10 10 1 7 21 35 35 1 9 36 84 126 126 1 11 55 165 330 462 462 1 13 78 286 715 1287
StdAntiDiagsee docsmissing1 0 0 1 0 2 0 5 1 0 14 4 0 42 14 1 0 132 48 6 0 429 165 27 1 0 1430 572 110 8 0 4862 2002 429 44 1
StdDiffx1T(n, k) (k+1)missing1 0 2 0 4 3 0 10 12 4 0 28 42 24 5 0 84 144 108 40 6 0 264 495 440 220 60 7 0 858 1716 1716 1040
StdRowSum k=0..n T(n, k)A0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
StdEvenSum k=0..n T(n, k) even(k)A0017911 0 1 4 15 56 210 792 3003 11440 43758 167960 646646 2496144 9657700 37442160 145422675 565722720
StdOddSum k=0..n T(n, k) odd(k)A0009840 1 2 6 20 70 252 924 3432 12870 48620 184756 705432 2704156 10400600 40116600 155117520 601080390
StdAltSum k=0..n T(n, k) (-1)^kA0001081 -1 -1 -2 -5 -14 -42 -132 -429 -1430 -4862 -16796 -58786 -208012 -742900 -2674440 -9694845
StdAbsSum k=0..n | T(n, k) |A0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
StdDiagSum k=0..n // 2 T(n - k, k)A0009571 0 1 2 6 18 57 186 622 2120 7338 25724 91144 325878 1174281 4260282 15548694 57048048 210295326
StdAccSum k=0..n j=0..k T(n, j)A2967701 1 5 24 111 500 2210 9632 41531 177564 754014 3184016 13382710 56026984 233765636 972504704
StdAccRevSum k=0..n j=0..k T(n, n - j)A1141211 2 7 26 99 382 1486 5812 22819 89846 354522 1401292 5546382 21977516 87167164 345994216 1374282019
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 20 42 3024 660 34320 450450 13613600 4232592 1777688640 240253860 144152316000 516300642000
StdRowGcdGcd k=0..n | T(n, k) | > 1A2973821 1 2 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
StdRowMaxMax k=0..n | T(n, k) |missing1 1 2 5 14 48 165 572 2002 7072 25194 90440 326876 1225785 4601610 17298645 65132550 245642760
StdColMiddleT(n, n // 2)missing1 0 2 5 14 48 110 429 910 3808 7752 33915 67298 303600 592020 2731365 5259150 24682944 47071640
StdCentralET(2 n, n)A3591081 2 14 110 910 7752 67298 592020 5259150 47071640 423830264 3834669566 34834267234 317506779800
StdCentralOT(2 n + 1, n)missing0 5 48 429 3808 33915 303600 2731365 24682944 223926516 2038362560 18609425835 170333048928
StdColLeftT(n, 0)A0000071 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
StdColRightT(n, n)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdBinConv k=0..n C(n, k) T(n, k)A0251741 1 5 28 165 1001 6188 38760 245157 1562275 10015005 64512240 417225900 2707475148 17620076360
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 1 -3 4 5 -39 84 8 -603 1795 -1243 -9096 37388 -50036 -119640 747984 -1460827 -1006569 14187927
StdTransNat0 k=0..n T(n, k) kA0003020 1 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824
StdTransNat1 k=0..n T(n, k) (k + 1)A1141211 2 7 26 99 382 1486 5812 22819 89846 354522 1401292 5546382 21977516 87167164 345994216 1374282019
StdTransSqrs k=0..n T(n, k) k^2A0024570 1 6 30 140 630 2772 12012 51480 218790 923780 3879876 16224936 67603900 280816200 1163381400
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kA1947231 1 5 29 181 1181 7941 54573 381333 2699837 19319845 139480397 1014536117 7426790749 54669443141
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0640621 1 -3 13 -67 381 -2307 14589 -95235 636925 -4341763 30056445 -210731011 1493303293 -10678370307
StdDiagRow1T(n + 1, n)A0058430 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68
StdDiagRow2T(n + 2, n)A0141060 5 14 27 44 65 90 119 152 189 230 275 324 377 434 495 560 629 702 779 860 945 1034 1127 1224 1325
StdDiagRow3T(n + 3, n)missing0 14 48 110 208 350 544 798 1120 1518 2000 2574 3248 4030 4928 5950 7104 8398 9840 11438 13200
StdDiagCol1T(n + 1, 1)A0001081 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790
StdDiagCol2T(n + 2, 2)A0020571 4 14 48 165 572 2002 7072 25194 90440 326876 1188640 4345965 15967980 58929450 218349120
StdDiagCol3T(n + 3, 3)A0035171 6 27 110 429 1638 6188 23256 87210 326876 1225785 4601610 17298645 65132550 245642760 927983760
StdPolysee docsmissing1 0 1 0 1 1 0 3 2 1 0 10 8 3 1 0 35 34 15 4 1 0 126 148 78 24 5 1 0 462 652 411 148 35 6 1 0 1716
StdPolyRow1 k=0..1 T(1, k) n^kA0000270 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
StdPolyRow2 k=0..2 T(2, k) n^kA0055630 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
StdPolyRow3 k=0..3 T(3, k) n^kmissing0 10 34 78 148 250 390 574 808 1098 1450 1870 2364 2938 3598 4350 5200 6154 7218 8398 9700 11130
StdPolyCol2 k=0..n T(n, k) 2^kA0673361 2 8 34 148 652 2892 12882 57540 257500 1153888 5175700 23231864 104335376 468766292 2106773874
StdPolyCol3 k=0..n T(n, k) 3^kA1045301 3 15 78 411 2178 11574 61596 328083 1748346 9319650 49688004 264943902 1412826132 7534329804
StdPolyDiag k=0..n T(n, k) n^kmissing1 1 8 78 920 12910 211932 4005372 85904688 2064940470 55043183360 1612451393476 51512761928784
AltTriangleT(n, k), 0 ≤ k ≤ nA1288991 0 -1 0 -2 1 0 -5 4 -1 0 -14 14 -6 1 0 -42 48 -27 8 -1 0 -132 165 -110 44 -10 1 0 -429 572 -429
AltRevT(n, n - k), 0 ≤ k ≤ nmissing1 -1 0 1 -2 0 -1 4 -5 0 1 -6 14 -14 0 -1 8 -27 48 -42 0 1 -10 44 -110 165 -132 0 -1 12 -65 208 -429
AltInvT-1(n, k), 0 ≤ k ≤ nmissing1 0 1 0 2 1 0 -3 -4 1 0 -32 -38 6 1 0 121 148 -21 -8 1 0 2090 2547 -364 -124 10 1 0 -12561 -15328
AltRevInvT-1(n, n - k), 0 ≤ k ≤ nmissing1 1 0 1 2 0 1 -4 -3 0 1 6 -38 -32 0 1 -8 -21 148 121 0 1 10 -124 -364 2547 2090 0 1 -12 -55 760
AltAccsee docsmissing1 0 -1 0 -2 -1 0 -5 -1 -2 0 -14 0 -6 -5 0 -42 6 -21 -13 -14 0 -132 33 -77 -33 -43 -42 0 -429 143
AltAccRevsee docsmissing1 -1 -1 1 -1 -1 -1 3 -2 -2 1 -5 9 -5 -5 -1 7 -20 28 -14 -14 1 -9 35 -75 90 -42 -42 -1 11 -54 154
AltAntiDiagsee docsmissing1 0 0 -1 0 -2 0 -5 1 0 -14 4 0 -42 14 -1 0 -132 48 -6 0 -429 165 -27 1 0 -1430 572 -110 8 0 -4862
AltDiffx1T(n, k) (k+1)missing1 0 -2 0 -4 3 0 -10 12 -4 0 -28 42 -24 5 0 -84 144 -108 40 -6 0 -264 495 -440 220 -60 7 0 -858 1716
AltRowSum k=0..n T(n, k)A0001081 -1 -1 -2 -5 -14 -42 -132 -429 -1430 -4862 -16796 -58786 -208012 -742900 -2674440 -9694845
AltEvenSum k=0..n T(n, k) even(k)A0017911 0 1 4 15 56 210 792 3003 11440 43758 167960 646646 2496144 9657700 37442160 145422675 565722720
AltOddSum k=0..n T(n, k) odd(k)A0009840 -1 -2 -6 -20 -70 -252 -924 -3432 -12870 -48620 -184756 -705432 -2704156 -10400600 -40116600
AltAltSum k=0..n T(n, k) (-1)^kA0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
AltAbsSum k=0..n | T(n, k) |A0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
AltDiagSum k=0..n // 2 T(n - k, k)A1353341 0 -1 -2 -4 -10 -29 -90 -290 -960 -3246 -11164 -38934 -137358 -489341 -1757882 -6360634 -23160528
AltAccSum k=0..n j=0..k T(n, j)A0386651 -1 -3 -8 -25 -84 -294 -1056 -3861 -14300 -53482 -201552 -764218 -2912168 -11143500 -42791040
AltAccRevSum k=0..n j=0..k T(n, n - j)A0001081 -2 -1 -2 -5 -14 -42 -132 -429 -1430 -4862 -16796 -58786 -208012 -742900 -2674440 -9694845
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 20 42 3024 660 34320 450450 13613600 4232592 1777688640 240253860 144152316000 516300642000
AltRowGcdGcd k=0..n | T(n, k) | > 1A2973821 1 2 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
AltRowMaxMax k=0..n | T(n, k) |missing1 1 2 5 14 48 165 572 2002 7072 25194 90440 326876 1225785 4601610 17298645 65132550 245642760
AltColMiddleT(n, n // 2)missing1 0 -2 -5 14 48 -110 -429 910 3808 -7752 -33915 67298 303600 -592020 -2731365 5259150 24682944
AltCentralET(2 n, n)A3591081 -2 14 -110 910 -7752 67298 -592020 5259150 -47071640 423830264 -3834669566 34834267234
AltCentralOT(2 n + 1, n)missing0 -5 48 -429 3808 -33915 303600 -2731365 24682944 -223926516 2038362560 -18609425835 170333048928
AltColLeftT(n, 0)A0000071 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
AltBinConv k=0..n C(n, k) T(n, k)missing1 -1 -3 -4 5 39 84 -8 -603 -1795 -1243 9096 37388 50036 -119640 -747984 -1460827 1006569 14187927
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA0251741 -1 5 -28 165 -1001 6188 -38760 245157 -1562275 10015005 -64512240 417225900 -2707475148
AltTransNat0 k=0..n T(n, k) kA0635240 -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
AltTransNat1 k=0..n T(n, k) (k + 1)A0001081 -2 -1 -2 -5 -14 -42 -132 -429 -1430 -4862 -16796 -58786 -208012 -742900 -2674440 -9694845
AltTransSqrs k=0..n T(n, k) k^2A0688750 -1 2 2 4 10 28 84 264 858 2860 9724 33592 117572 416024 1485800 5348880 19389690 70715340
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kA0640621 -1 -3 -13 -67 -381 -2307 -14589 -95235 -636925 -4341763 -30056445 -210731011 -1493303293
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA1947231 -1 5 -29 181 -1181 7941 -54573 381333 -2699837 19319845 -139480397 1014536117 -7426790749
AltDiagRow1T(n + 1, n)A0058430 -2 4 -6 8 -10 12 -14 16 -18 20 -22 24 -26 28 -30 32 -34 36 -38 40 -42 44 -46 48 -50 52 -54 56 -58
AltDiagRow2T(n + 2, n)A0141060 -5 14 -27 44 -65 90 -119 152 -189 230 -275 324 -377 434 -495 560 -629 702 -779 860 -945 1034
AltDiagRow3T(n + 3, n)missing0 -14 48 -110 208 -350 544 -798 1120 -1518 2000 -2574 3248 -4030 4928 -5950 7104 -8398 9840 -11438
AltDiagCol1T(n + 1, 1)A000108-1 -2 -5 -14 -42 -132 -429 -1430 -4862 -16796 -58786 -208012 -742900 -2674440 -9694845 -35357670
AltDiagCol2T(n + 2, 2)A0020571 4 14 48 165 572 2002 7072 25194 90440 326876 1188640 4345965 15967980 58929450 218349120
AltDiagCol3T(n + 3, 3)A003517-1 -6 -27 -110 -429 -1638 -6188 -23256 -87210 -326876 -1225785 -4601610 -17298645 -65132550
AltPolysee docsmissing1 0 1 0 -1 1 0 -1 -2 1 0 -2 0 -3 1 0 -5 -2 3 -4 1 0 -14 -4 -6 8 -5 1 0 -42 -12 3 -20 15 -6 1 0 -132
AltPolyRow1 k=0..1 T(1, k) n^kA0000270 -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
AltPolyRow2 k=0..2 T(2, k) n^kA0055630 -1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728
AltPolyRow3 k=0..3 T(3, k) n^kmissing0 -2 -2 -6 -20 -50 -102 -182 -296 -450 -650 -902 -1212 -1586 -2030 -2550 -3152 -3842 -4626 -5510
AltPolyCol2 k=0..n T(n, k) 2^kmissing1 -2 0 -2 -4 -12 -36 -114 -372 -1244 -4240 -14676 -51448 -182288 -651756 -2348562 -8520564
AltPolyCol3 k=0..n T(n, k) 3^kmissing1 -3 3 -6 3 -18 -18 -108 -285 -1050 -3462 -12180 -42546 -151284 -541188 -1952856 -7091037 -25902954
AltPolyDiag k=0..n T(n, k) n^kmissing1 -1 0 -6 40 -510 7308 -126924 2546640 -58123350 1485935440 -42059272596 1305569973552
RevTriangleT(n, k), 0 ≤ k ≤ nmissing1 1 0 1 2 0 1 4 5 0 1 6 14 14 0 1 8 27 48 42 0 1 10 44 110 165 132 0 1 12 65 208 429 572 429 0 1 14
RevInvRev(T(n, n - k))-1, 0 ≤ k ≤ nA1289081 0 1 0 -2 1 0 3 -4 1 0 -4 10 -6 1 0 5 -20 21 -8 1 0 -6 35 -56 36 -10 1 0 7 -56 126 -120 55 -12 1 0
RevAccsee docsmissing1 1 1 1 3 3 1 5 10 10 1 7 21 35 35 1 9 36 84 126 126 1 11 55 165 330 462 462 1 13 78 286 715 1287
RevAccRevsee docsmissing1 0 1 0 2 3 0 5 9 10 0 14 28 34 35 0 42 90 117 125 126 0 132 297 407 451 461 462 0 429 1001 1430
RevAntiDiagsee docsmissing1 1 1 0 1 2 1 4 0 1 6 5 1 8 14 0 1 10 27 14 1 12 44 48 0 1 14 65 110 42 1 16 90 208 165 0 1 18 119
RevDiffx1T(n, k) (k+1)missing1 1 0 1 4 0 1 8 15 0 1 12 42 56 0 1 16 81 192 210 0 1 20 132 440 825 792 0 1 24 195 832 2145 3432
RevRowSum k=0..n T(n, k)A0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
RevEvenSum k=0..n T(n, k) even(k)missing1 1 1 6 15 70 210 924 3003 12870 43758 184756 646646 2704156 9657700 40116600 145422675 601080390
RevOddSum k=0..n T(n, k) odd(k)missing0 0 2 4 20 56 252 792 3432 11440 48620 167960 705432 2496144 10400600 37442160 155117520 565722720
RevAltSum k=0..n T(n, k) (-1)^kA0001081 1 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670
RevAbsSum k=0..n | T(n, k) |A0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
RevDiagSum k=0..n // 2 T(n - k, k)A2247471 1 1 3 5 12 23 52 105 232 480 1049 2199 4777 10092 21845 46377 100159 213328 460023 981976 2115350
RevAccSum k=0..n j=0..k T(n, j)A1141211 2 7 26 99 382 1486 5812 22819 89846 354522 1401292 5546382 21977516 87167164 345994216 1374282019
RevAccRevSum k=0..n j=0..k T(n, n - j)A2967701 1 5 24 111 500 2210 9632 41531 177564 754014 3184016 13382710 56026984 233765636 972504704
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 20 42 3024 660 34320 450450 13613600 4232592 1777688640 240253860 144152316000 516300642000
RevRowGcdGcd k=0..n | T(n, k) | > 1A2973821 1 2 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
RevRowMaxMax k=0..n | T(n, k) |missing1 1 2 5 14 48 165 572 2002 7072 25194 90440 326876 1225785 4601610 17298645 65132550 245642760
RevColMiddleT(n, n // 2)missing1 1 2 4 14 27 110 208 910 1700 7752 14364 67298 123970 592020 1085760 5259150 9612108 47071640
RevCentralET(2 n, n)A3591081 2 14 110 910 7752 67298 592020 5259150 47071640 423830264 3834669566 34834267234 317506779800
RevCentralOT(2 n + 1, n)A0260051 4 27 208 1700 14364 123970 1085760 9612108 85795600 770755843 6960408624 63127818572 574609830760
RevColLeftT(n, 0)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
RevColRightT(n, n)A0000071 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
RevBinConv k=0..n C(n, k) T(n, k)A0251741 1 5 28 165 1001 6188 38760 245157 1562275 10015005 64512240 417225900 2707475148 17620076360
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 -3 -4 5 39 84 -8 -603 -1795 -1243 9096 37388 50036 -119640 -747984 -1460827 1006569 14187927
RevTransNat0 k=0..n T(n, k) kA1720600 0 2 14 76 374 1748 7916 35096 153254 661636 2831300 12030632 50826684 213707336 894945944
RevTransNat1 k=0..n T(n, k) (k + 1)A2967701 1 5 24 111 500 2210 9632 41531 177564 754014 3184016 13382710 56026984 233765636 972504704
RevTransSqrs k=0..n T(n, k) k^2missing0 0 2 24 188 1220 7116 38752 201176 1008252 4918700 23489840 110260872 510246984 2333194808
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA0673361 2 8 34 148 652 2892 12882 57540 257500 1153888 5175700 23231864 104335376 468766292 2106773874
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 -2 0 -2 -4 -12 -36 -114 -372 -1244 -4240 -14676 -51448 -182288 -651756 -2348562 -8520564
RevDiagRow1T(n + 1, n)A0001081 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790
RevDiagRow2T(n + 2, n)A0020571 4 14 48 165 572 2002 7072 25194 90440 326876 1188640 4345965 15967980 58929450 218349120
RevDiagRow3T(n + 3, n)A0035171 6 27 110 429 1638 6188 23256 87210 326876 1225785 4601610 17298645 65132550 245642760 927983760
RevDiagCol1T(n + 1, 1)A0058430 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68
RevDiagCol2T(n + 2, 2)A0141060 5 14 27 44 65 90 119 152 189 230 275 324 377 434 495 560 629 702 779 860 945 1034 1127 1224 1325
RevDiagCol3T(n + 3, 3)missing0 14 48 110 208 350 544 798 1120 1518 2000 2574 3248 4030 4928 5950 7104 8398 9840 11438 13200
RevPolysee docsmissing1 1 1 1 1 1 1 3 1 1 1 10 5 1 1 1 35 29 7 1 1 1 126 181 58 9 1 1 1 462 1181 523 97 11 1 1 1 1716
RevPolyRow1 k=0..1 T(1, k) n^kA0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
RevPolyRow2 k=0..2 T(2, k) n^kA0054081 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69
RevPolyRow3 k=0..3 T(3, k) n^kA0792731 10 29 58 97 146 205 274 353 442 541 650 769 898 1037 1186 1345 1514 1693 1882 2081 2290 2509 2738
RevPolyCol2 k=0..n T(n, k) 2^kA1947231 1 5 29 181 1181 7941 54573 381333 2699837 19319845 139480397 1014536117 7426790749 54669443141
RevPolyCol3 k=0..n T(n, k) 3^kA1947241 1 7 58 523 4966 48838 492724 5068915 52955950 560198962 5987822380 64563867454 701383563388
RevPolyDiag k=0..n T(n, k) n^kmissing1 1 5 58 1145 32966 1265677 61189668 3581326065 246643289830 19564269083381 1757975451672716
InvTriangleT(n, k), 0 ≤ k ≤ nA1289081 0 1 0 -2 1 0 3 -4 1 0 -4 10 -6 1 0 5 -20 21 -8 1 0 -6 35 -56 36 -10 1 0 7 -56 126 -120 55 -12 1 0
InvRevT(n, n - k), 0 ≤ k ≤ nmissing1 1 0 1 -2 0 1 -4 3 0 1 -6 10 -4 0 1 -8 21 -20 5 0 1 -10 36 -56 35 -6 0 1 -12 55 -120 126 -56 7 0 1
InvRevInvT-1(n, n - k), 0 ≤ k ≤ nmissing1 1 0 1 2 0 1 4 5 0 1 6 14 14 0 1 8 27 48 42 0 1 10 44 110 165 132 0 1 12 65 208 429 572 429 0 1 14
InvAccsee docsmissing1 0 1 0 -2 -1 0 3 -1 0 0 -4 6 0 1 0 5 -15 6 -2 -1 0 -6 29 -27 9 -1 0 0 7 -49 77 -43 12 0 1 0 -8 76
InvAccRevsee docsmissing1 1 1 1 -1 -1 1 -3 0 0 1 -5 5 1 1 1 -7 14 -6 -1 -1 1 -9 27 -29 6 0 0 1 -11 44 -76 50 -6 1 1 1 -13
InvAntiDiagsee docsmissing1 0 0 1 0 -2 0 3 1 0 -4 -4 0 5 10 1 0 -6 -20 -6 0 7 35 21 1 0 -8 -56 -56 -8 0 9 84 126 36 1 0 -10
InvDiffx1T(n, k) (k+1)missing1 0 2 0 -4 3 0 6 -12 4 0 -8 30 -24 5 0 10 -60 84 -40 6 0 -12 105 -224 180 -60 7 0 14 -168 504 -600
InvRowSum k=0..n T(n, k)A3296821 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
InvEvenSum k=0..n T(n, k) even(k)A2908901 0 1 -4 11 -28 72 -188 493 -1292 3383 -8856 23184 -60696 158905 -416020 1089155 -2851444 7465176
InvOddSum k=0..n T(n, k) odd(k)A1130660 1 -2 4 -10 27 -72 189 -494 1292 -3382 8855 -23184 60697 -158906 416020 -1089154 2851443 -7465176
InvAltSum k=0..n T(n, k) (-1)^kA0019061 -1 3 -8 21 -55 144 -377 987 -2584 6765 -17711 46368 -121393 317811 -832040 2178309 -5702887
InvAbsSum k=0..n | T(n, k) |A0019061 1 3 8 21 55 144 377 987 2584 6765 17711 46368 121393 317811 832040 2178309 5702887 14930352
InvDiagSum k=0..n // 2 T(n - k, k)A0000791 0 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144
InvAccSum k=0..n j=0..k T(n, j)A3320571 1 -3 2 3 -7 4 5 -11 6 7 -15 8 9 -19 10 11 -23 12 13 -27 14 15 -31 16 17 -35 18 19 -39 20 21 -43
InvAccRevSum k=0..n j=0..k T(n, n - j)A1372411 2 -1 -2 3 0 -4 4 1 -6 5 2 -8 6 3 -10 7 4 -12 8 5 -14 9 6 -16 10 7 -18 11 8 -20 12 9 -22 13 10 -24
InvRowLcmLcm k=0..n | T(n, k) | > 1A0999961 1 2 12 60 840 2520 27720 360360 720720 12252240 232792560 232792560 5354228880 26771144400
InvRowGcdGcd k=0..n | T(n, k) | > 1A2973821 1 2 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
InvRowMaxMax k=0..n | T(n, k) |missing1 1 2 4 10 21 56 126 330 792 2002 5005 12376 31824 77520 203490 497420 1307504 3268760 8436285
InvColMiddleT(n, n // 2)missing1 0 -2 3 10 -20 -56 126 330 -792 -2002 5005 12376 -31824 -77520 203490 490314 -1307504 -3124550
InvCentralET(2 n, n)A1658171 -2 10 -56 330 -2002 12376 -77520 490314 -3124550 20030010 -129024480 834451800 -5414950296
InvCentralOT(2 n + 1, n)missing0 3 -20 126 -792 5005 -31824 203490 -1307504 8436285 -54627300 354817320 -2310789600 15084504396
InvColLeftT(n, 0)A0000071 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
InvColRightT(n, n)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
InvBinConv k=0..n C(n, k) T(n, k)A3502901 1 -3 -2 21 -4 -150 155 1029 -2072 -6468 22056 34122 -208857 -106249 1816958 -639067 -14629264
InvInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA2624401 1 5 22 101 476 2282 11075 54245 267592 1327580 6617128 33110090 166215895 836761343 4222640822
InvTransNat0 k=0..n T(n, k) kA1229180 1 0 -2 2 1 -4 3 2 -6 4 3 -8 5 4 -10 6 5 -12 7 6 -14 8 7 -16 9 8 -18 10 9 -20 11 10 -22 12 11 -24
InvTransNat1 k=0..n T(n, k) (k + 1)A1372411 2 -1 -2 3 0 -4 4 1 -6 5 2 -8 6 3 -10 7 4 -12 8 5 -14 9 6 -16 10 7 -18 11 8 -20 12 9 -22 13 10 -24
InvTransSqrs k=0..n T(n, k) k^2missing0 1 2 -4 -2 11 -8 -11 26 -12 -26 47 -16 -47 74 -20 -74 107 -24 -107 146 -28 -146 191 -32 -191 242
InvPosHalf k=0..n 2^n T(n, k) (1/2)^kA0490721 1 -3 5 -3 -11 45 -91 93 85 -627 1541 -2115 181 7917 -24475 41757 -27371 -84915 364229 -753027
InvNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0024501 1 5 21 85 341 1365 5461 21845 87381 349525 1398101 5592405 22369621 89478485 357913941 1431655765
InvDiagRow1T(n + 1, n)A0058430 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36 -38 -40 -42 -44 -46 -48 -50
InvDiagRow2T(n + 2, n)A0141050 3 10 21 36 55 78 105 136 171 210 253 300 351 406 465 528 595 666 741 820 903 990 1081 1176 1275
InvDiagRow3T(n + 3, n)A0024920 -4 -20 -56 -120 -220 -364 -560 -816 -1140 -1540 -2024 -2600 -3276 -4060 -4960 -5984 -7140 -8436
InvDiagCol1T(n + 1, 1)A0000271 -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
InvDiagCol2T(n + 2, 2)A0002921 -4 10 -20 35 -56 84 -120 165 -220 286 -364 455 -560 680 -816 969 -1140 1330 -1540 1771 -2024 2300
InvDiagCol3T(n + 3, 3)A0003891 -6 21 -56 126 -252 462 -792 1287 -2002 3003 -4368 6188 -8568 11628 -15504 20349 -26334 33649
InvPolysee docsmissing1 0 1 0 1 1 0 -1 2 1 0 0 0 3 1 0 1 -2 3 4 1 0 -1 0 0 8 5 1 0 0 2 -3 12 15 6 1 0 1 0 -3 16 40 24 7 1
InvPolyRow1 k=0..1 T(1, k) n^kA0000270 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
InvPolyRow2 k=0..2 T(2, k) n^kA0055630 -1 0 3 8 15 24 35 48 63 80 99 120 143 168 195 224 255 288 323 360 399 440 483 528 575 624 675 728
InvPolyRow3 k=0..3 T(3, k) n^kmissing0 0 -2 0 12 40 90 168 280 432 630 880 1188 1560 2002 2520 3120 3808 4590 5472 6460 7560 8778 10120
InvPolyCol2 k=0..n T(n, k) 2^kA0106731 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 -2
InvPolyCol3 k=0..n T(n, k) 3^kA0998381 3 3 0 -3 -3 0 3 3 0 -3 -3 0 3 3 0 -3 -3 0 3 3 0 -3 -3 0 3 3 0 -3 -3 0 3 3 0 -3 -3 0 3 3 0 -3 -3 0
InvPolyDiag k=0..n T(n, k) n^kmissing1 1 0 0 16 275 4680 88543 1883328 44791056 1181184400 34254174229 1084253219280 37213995870493
Inv:RevTriangleT(n, k), 0 ≤ k ≤ nmissing1 1 0 1 -2 0 1 -4 3 0 1 -6 10 -4 0 1 -8 21 -20 5 0 1 -10 36 -56 35 -6 0 1 -12 55 -120 126 -56 7 0 1
Inv:RevRevT(n, n - k), 0 ≤ k ≤ nA1289081 0 1 0 -2 1 0 3 -4 1 0 -4 10 -6 1 0 5 -20 21 -8 1 0 -6 35 -56 36 -10 1 0 7 -56 126 -120 55 -12 1 0
Inv:RevInvRev(T(n, n - k))-1, 0 ≤ k ≤ nA1288991 0 1 0 2 1 0 5 4 1 0 14 14 6 1 0 42 48 27 8 1 0 132 165 110 44 10 1 0 429 572 429 208 65 12 1 0
Inv:RevAccsee docsmissing1 1 1 1 -1 -1 1 -3 0 0 1 -5 5 1 1 1 -7 14 -6 -1 -1 1 -9 27 -29 6 0 0 1 -11 44 -76 50 -6 1 1 1 -13
Inv:RevAccRevsee docsmissing1 0 1 0 -2 -1 0 3 -1 0 0 -4 6 0 1 0 5 -15 6 -2 -1 0 -6 29 -27 9 -1 0 0 7 -49 77 -43 12 0 1 0 -8 76
Inv:RevAntiDiagsee docsmissing1 1 1 0 1 -2 1 -4 0 1 -6 3 1 -8 10 0 1 -10 21 -4 1 -12 36 -20 0 1 -14 55 -56 5 1 -16 78 -120 35 0 1
Inv:RevDiffx1T(n, k) (k+1)missing1 1 0 1 -4 0 1 -8 9 0 1 -12 30 -16 0 1 -16 63 -80 25 0 1 -20 108 -224 175 -36 0 1 -24 165 -480 630
Inv:RevRowSum k=0..n T(n, k)A3296821 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0
Inv:RevEvenSum k=0..n T(n, k) even(k)A3767161 1 1 4 11 27 72 189 493 1292 3383 8855 23184 60697 158905 416020 1089155 2851443 7465176 19544085
Inv:RevOddSum k=0..n T(n, k) odd(k)missing0 0 -2 -4 -10 -28 -72 -188 -494 -1292 -3382 -8856 -23184 -60696 -158906 -416020 -1089154 -2851444
Inv:RevAltSum k=0..n T(n, k) (-1)^kA0019061 1 3 8 21 55 144 377 987 2584 6765 17711 46368 121393 317811 832040 2178309 5702887 14930352
Inv:RevAbsSum k=0..n | T(n, k) |A0019061 1 3 8 21 55 144 377 987 2584 6765 17711 46368 121393 317811 832040 2178309 5702887 14930352
Inv:RevDiagSum k=0..n // 2 T(n - k, k)missing1 1 1 -1 -3 -2 3 8 5 -9 -22 -12 27 60 28 -80 -163 -63 235 441 134 -685 -1188 -259 1983 3186 408
Inv:RevAccSum k=0..n j=0..k T(n, j)A1372411 2 -1 -2 3 0 -4 4 1 -6 5 2 -8 6 3 -10 7 4 -12 8 5 -14 9 6 -16 10 7 -18 11 8 -20 12 9 -22 13 10 -24
Inv:RevAccRevSum k=0..n j=0..k T(n, n - j)A3320571 1 -3 2 3 -7 4 5 -11 6 7 -15 8 9 -19 10 11 -23 12 13 -27 14 15 -31 16 17 -35 18 19 -39 20 21 -43
Inv:RevRowLcmLcm k=0..n | T(n, k) | > 1A0999961 1 2 12 60 840 2520 27720 360360 720720 12252240 232792560 232792560 5354228880 26771144400
Inv:RevRowGcdGcd k=0..n | T(n, k) | > 1A2973821 1 2 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:RevRowMaxMax k=0..n | T(n, k) |missing1 1 2 4 10 21 56 126 330 792 2002 5005 12376 31824 77520 203490 497420 1307504 3268760 8436285
Inv:RevColMiddleT(n, n // 2)missing1 1 -2 -4 10 21 -56 -120 330 715 -2002 -4368 12376 27132 -77520 -170544 490314 1081575 -3124550
Inv:RevCentralET(2 n, n)A1658171 -2 10 -56 330 -2002 12376 -77520 490314 -3124550 20030010 -129024480 834451800 -5414950296
Inv:RevCentralOT(2 n + 1, n)A0457211 -4 21 -120 715 -4368 27132 -170544 1081575 -6906900 44352165 -286097760 1852482996 -12033222880
Inv:RevColLeftT(n, 0)A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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:RevColRightT(n, n)A0000071 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:RevBinConv k=0..n C(n, k) T(n, k)A3502901 1 -3 -2 21 -4 -150 155 1029 -2072 -6468 22056 34122 -208857 -106249 1816958 -639067 -14629264
Inv:RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA2624401 -1 5 -22 101 -476 2282 -11075 54245 -267592 1327580 -6617128 33110090 -166215895 836761343
Inv:RevTransNat1 k=0..n T(n, k) (k + 1)A3320571 1 -3 2 3 -7 4 5 -11 6 7 -15 8 9 -19 10 11 -23 12 13 -27 14 15 -31 16 17 -35 18 19 -39 20 21 -43
Inv:RevTransSqrs k=0..n T(n, k) k^2missing0 0 -2 8 -2 -24 40 -4 -70 96 -6 -140 176 -8 -234 280 -10 -352 408 -12 -494 560 -14 -660 736 -16
Inv:RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA0106731 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 -2
Inv:RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0525301 -2 8 -30 112 -418 1560 -5822 21728 -81090 302632 -1129438 4215120 -15731042 58709048 -219105150
Inv:RevDiagRow1T(n + 1, n)A0000271 -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
Inv:RevDiagRow2T(n + 2, n)A0002921 -4 10 -20 35 -56 84 -120 165 -220 286 -364 455 -560 680 -816 969 -1140 1330 -1540 1771 -2024 2300
Inv:RevDiagRow3T(n + 3, n)A0003891 -6 21 -56 126 -252 462 -792 1287 -2002 3003 -4368 6188 -8568 11628 -15504 20349 -26334 33649
Inv:RevDiagCol1T(n + 1, 1)A0058430 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36 -38 -40 -42 -44 -46 -48 -50
Inv:RevDiagCol2T(n + 2, 2)A0141050 3 10 21 36 55 78 105 136 171 210 253 300 351 406 465 528 595 666 741 820 903 990 1081 1176 1275
Inv:RevDiagCol3T(n + 3, 3)A0024920 -4 -20 -56 -120 -220 -364 -560 -816 -1140 -1540 -2024 -2600 -3276 -4060 -4960 -5984 -7140 -8436
Inv:RevPolysee docsmissing1 1 1 1 1 1 1 -1 1 1 1 0 -3 1 1 1 1 5 -5 1 1 1 -1 -3 16 -7 1 1 1 0 -11 -35 33 -9 1 1 1 1 45 31 -119
Inv:RevPolyRow1 k=0..1 T(1, k) n^kA0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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:RevPolyRow2 k=0..2 T(2, k) n^kA0054081 -1 -3 -5 -7 -9 -11 -13 -15 -17 -19 -21 -23 -25 -27 -29 -31 -33 -35 -37 -39 -41 -43 -45 -47 -49
Inv:RevPolyRow3 k=0..3 T(3, k) n^kA0459441 0 5 16 33 56 85 120 161 208 261 320 385 456 533 616 705 800 901 1008 1121 1240 1365 1496 1633
Inv:RevPolyCol2 k=0..n T(n, k) 2^kA0490721 1 -3 5 -3 -11 45 -91 93 85 -627 1541 -2115 181 7917 -24475 41757 -27371 -84915 364229 -753027
Inv:RevPolyCol3 k=0..n T(n, k) 3^kA1909701 1 -5 16 -35 31 160 -1079 3955 -10064 14725 16951 -217280 933841 -2713685 5163856 -1396115
Inv:RevPolyDiag k=0..n T(n, k) n^kmissing1 1 -3 16 -119 1111 -12155 146329 -1770735 16657264 108903421 -16239940441 854302763545
 << TableSourceSimilarsIndex >> 

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.