FUBINI[0] 1
[1] 0, 1
[2] 0, 1, 2
[3] 0, 1, 6, 6
[4] 0, 1, 14, 36, 24
[5] 0, 1, 30, 150, 240, 120

      OEIS Similars: A131689, A019538, A090582, A278075

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA1316891 0 1 0 1 2 0 1 6 6 0 1 14 36 24 0 1 30 150 240 120 0 1 62 540 1560 1800 720 0 1 126 1806 8400
StdRevT(n, n - k), 0 ≤ k ≤ nmissing1 1 0 2 1 0 6 6 1 0 24 36 14 1 0 120 240 150 30 1 0 720 1800 1560 540 62 1 0 5040 15120 16800 8400
StdAccsee docsmissing1 0 1 0 1 3 0 1 7 13 0 1 15 51 75 0 1 31 181 421 541 0 1 63 603 2163 3963 4683 0 1 127 1933 10333
StdAccRevsee docsmissing1 1 1 2 3 3 6 12 13 13 24 60 74 75 75 120 360 510 540 541 541 720 2520 4080 4620 4682 4683 4683
StdAntiDiagsee docsA3443921 0 0 1 0 1 0 1 2 0 1 6 0 1 14 6 0 1 30 36 0 1 62 150 24 0 1 126 540 240 0 1 254 1806 1560 120 0 1
StdDiffx1T(n, k) (k+1)missing1 0 2 0 2 6 0 2 18 24 0 2 42 144 120 0 2 90 600 1200 720 0 2 186 2160 7800 10800 5040 0 2 378 7224
StdRowSum k=0..n T(n, k)A0006701 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381
StdEvenSum k=0..n T(n, k) even(k)A0528411 0 2 6 38 270 2342 23646 272918 3543630 51123782 811316286 14045783798 263429174190 5320671485222
StdOddSum k=0..n T(n, k) odd(k)A0896770 1 1 7 37 271 2341 23647 272917 3543631 51123781 811316287 14045783797 263429174191 5320671485221
StdAbsSum k=0..n | T(n, k) |A0006701 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381
StdDiagSum k=0..n // 2 T(n - k, k)A1057951 0 1 1 3 7 21 67 237 907 3741 16507 77517 385627 2024301 11174587 64673997 391392667 2470864941
StdAccSum k=0..n j=0..k T(n, j)A1203681 1 4 21 142 1175 11476 129073 1641802 23292459 364530688 6237123365 115806988342 2318774566303
StdAccRevSum k=0..n j=0..k T(n, n - j)A0056491 2 8 44 308 2612 25988 296564 3816548 54667412 862440068 14857100084 277474957988 5584100659412
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 6 504 1200 4352400 6501600 31719676464000 3839514683558400 6734455286856081120000
StdRowGcdGcd k=0..n | T(n, k) | > 1A0277601 1 2 6 2 30 2 42 2 30 2 66 2 2730 2 6 2 510 2 798 2 330 2 138 2 2730 2 6 2 870 2 14322 2 510 2 6 2
StdRowMaxMax k=0..n | T(n, k) |A0028691 1 2 6 36 240 1800 16800 191520 2328480 30240000 479001600 8083152000 142702560000 2731586457600
StdColMiddleT(n, n // 2)A3443971 0 1 1 14 30 540 1806 40824 186480 5103000 29607600 953029440 6711344640 248619571200
StdCentralET(2 n, n)A2100291 1 14 540 40824 5103000 953029440 248619571200 86355926616960 38528927611574400
StdCentralOT(2 n + 1, n)A3673920 1 30 1806 186480 29607600 6711344640 2060056318320 823172919528960 415357755774998400
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)A0001421 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200
StdBinConv k=0..n C(n, k) T(n, k)A0003121 1 4 27 256 3125 46656 823543 16777216 387420489 10000000000 285311670611 8916100448256
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA3440531 1 0 -9 -40 125 3444 18571 -241872 -5796711 -24387220 1132278191 25132445832 8850583573
StdTransNat0 k=0..n T(n, k) kA0693210 1 5 31 233 2071 21305 249271 3270713 47580151 760192505 13234467511 249383390393 5057242311031
StdTransNat1 k=0..n T(n, k) (k + 1)A0056491 2 8 44 308 2612 25988 296564 3816548 54667412 862440068 14857100084 277474957988 5584100659412
StdTransSqrs k=0..n T(n, k) k^2A0834110 1 9 79 765 8311 100989 1362439 20246445 328972471 5805917469 110645911399 2265191981325
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kA1227041 1 4 22 160 1456 15904 202672 2951680 48361216 880405504 17630351872 385148108800 9114999832576
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0090061 1 0 -2 0 16 0 -272 0 7936 0 -353792 0 22368256 0 -1903757312 0 209865342976 0 -29088885112832 0
StdDiagRow1T(n + 1, n)A0012860 1 6 36 240 1800 15120 141120 1451520 16329600 199584000 2634508800 37362124800 566658892800
StdDiagRow2T(n + 2, n)A0379600 1 14 150 1560 16800 191520 2328480 30240000 419126400 6187104000 97037740800 1612798387200
StdDiagRow3T(n + 3, n)A0379610 1 30 540 8400 126000 1905120 29635200 479001600 8083152000 142702560000 2637143308800
StdDiagCol1T(n + 1, 1)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
StdDiagCol2T(n + 2, 2)A0009182 6 14 30 62 126 254 510 1022 2046 4094 8190 16382 32766 65534 131070 262142 524286 1048574 2097150
StdDiagCol3T(n + 3, 3)A0011176 36 150 540 1806 5796 18150 55980 171006 519156 1569750 4733820 14250606 42850116 128746950
StdPolysee docsA3444991 0 1 0 1 1 0 3 2 1 0 13 10 3 1 0 75 74 21 4 1 0 541 730 219 36 5 1 0 4683 9002 3045 484 55 6 1 0
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^kA0141050 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
StdPolyRow3 k=0..3 T(3, k) n^kA0944210 13 74 219 484 905 1518 2359 3464 4869 6610 8723 11244 14209 17654 21615 26128 31229 36954 43339
StdPolyCol2 k=0..n T(n, k) 2^kA0041231 2 10 74 730 9002 133210 2299754 45375130 1007179562 24840104410 673895590634 19944372341530
StdPolyCol3 k=0..n T(n, k) 3^kA0320331 3 21 219 3045 52923 1103781 26857659 746870565 23365498683 812198635941 31055758599099
StdPolyDiag k=0..n T(n, k) n^kA0944201 1 10 219 8676 544505 49729758 6232661239 1026912225160 215270320769109 55954905981282210
AltAccsee docsmissing1 0 -1 0 -1 1 0 -1 5 -1 0 -1 13 -23 1 0 -1 29 -121 119 -1 0 -1 61 -479 1081 -719 1 0 -1 125 -1681
AltAccRevsee docsmissing1 -1 -1 2 1 1 -6 0 -1 -1 24 -12 2 1 1 -120 120 -30 0 -1 -1 720 -1080 480 -60 2 1 1 -5040 10080
AltAntiDiagsee docsA3443921 0 0 -1 0 -1 0 -1 2 0 -1 6 0 -1 14 -6 0 -1 30 -36 0 -1 62 -150 24 0 -1 126 -540 240 0 -1 254 -1806
AltDiffx1T(n, k) (k+1)missing1 0 -2 0 -2 6 0 -2 18 -24 0 -2 42 -144 120 0 -2 90 -600 1200 -720 0 -2 186 -2160 7800 -10800 5040 0
AltEvenSum k=0..n T(n, k) even(k)A0528411 0 2 6 38 270 2342 23646 272918 3543630 51123782 811316286 14045783798 263429174190 5320671485222
AltOddSum k=0..n T(n, k) odd(k)A0896770 -1 -1 -7 -37 -271 -2341 -23647 -272917 -3543631 -51123781 -811316287 -14045783797 -263429174191
AltAltSum k=0..n T(n, k) (-1)^kA0006701 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381
AltAbsSum k=0..n | T(n, k) |A0006701 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381
AltDiagSum k=0..n // 2 T(n - k, k)missing1 0 -1 -1 1 5 7 -7 -65 -175 -113 1313 7615 21665 3967 -351967 -2337665 -8401375 -5391233 176760353
AltAccSum k=0..n j=0..k T(n, j)A0002471 -1 0 3 -10 25 -56 119 -246 501 -1012 2035 -4082 8177 -16368 32751 -65518 131053 -262124 524267
AltAccRevSum k=0..n j=0..k T(n, n - j)A0000791 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 6 504 1200 4352400 6501600 31719676464000 3839514683558400 6734455286856081120000
AltRowGcdGcd k=0..n | T(n, k) | > 1A0277601 1 2 6 2 30 2 42 2 30 2 66 2 2730 2 6 2 510 2 798 2 330 2 138 2 2730 2 6 2 870 2 14322 2 510 2 6 2
AltRowMaxMax k=0..n | T(n, k) |A0028691 1 2 6 36 240 1800 16800 191520 2328480 30240000 479001600 8083152000 142702560000 2731586457600
AltColMiddleT(n, n // 2)A3443971 0 -1 -1 14 30 -540 -1806 40824 186480 -5103000 -29607600 953029440 6711344640 -248619571200
AltCentralET(2 n, n)A2100291 -1 14 -540 40824 -5103000 953029440 -248619571200 86355926616960 -38528927611574400
AltCentralOT(2 n + 1, n)A3673920 -1 30 -1806 186480 -29607600 6711344640 -2060056318320 823172919528960 -415357755774998400
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
AltColRightT(n, n)A0001421 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200
AltBinConv k=0..n C(n, k) T(n, k)A3440531 -1 0 9 -40 -125 3444 -18571 -241872 5796711 -24387220 -1132278191 25132445832 -8850583573
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA0003121 -1 4 -27 256 -3125 46656 -823543 16777216 -387420489 10000000000 -285311670611 8916100448256
AltTransNat0 k=0..n T(n, k) kA0002250 -1 3 -7 15 -31 63 -127 255 -511 1023 -2047 4095 -8191 16383 -32767 65535 -131071 262143 -524287
AltTransNat1 k=0..n T(n, k) (k + 1)A0000791 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288
AltTransSqrs k=0..n T(n, k) k^2A0913440 -1 7 -31 115 -391 1267 -3991 12355 -37831 115027 -348151 1050595 -3164071 9516787 -28599511
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kA0090061 -1 0 2 0 -16 0 272 0 -7936 0 353792 0 -22368256 0 1903757312 0 -209865342976 0 29088885112832 0
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA1227041 -1 4 -22 160 -1456 15904 -202672 2951680 -48361216 880405504 -17630351872 385148108800
AltDiagRow1T(n + 1, n)A0012860 -1 6 -36 240 -1800 15120 -141120 1451520 -16329600 199584000 -2634508800 37362124800
AltDiagRow2T(n + 2, n)A0379600 -1 14 -150 1560 -16800 191520 -2328480 30240000 -419126400 6187104000 -97037740800 1612798387200
AltDiagRow3T(n + 3, n)A0379610 -1 30 -540 8400 -126000 1905120 -29635200 479001600 -8083152000 142702560000 -2637143308800
AltDiagCol1T(n + 1, 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
AltDiagCol2T(n + 2, 2)A0009182 6 14 30 62 126 254 510 1022 2046 4094 8190 16382 32766 65534 131070 262142 524286 1048574 2097150
AltDiagCol3T(n + 3, 3)A001117-6 -36 -150 -540 -1806 -5796 -18150 -55980 -171006 -519156 -1569750 -4733820 -14250606 -42850116
AltPolysee docsmissing1 0 1 0 -1 1 0 1 -2 1 0 -1 6 -3 1 0 1 -26 15 -4 1 0 -1 150 -111 28 -5 1 0 1 -1082 1095 -292 45 -6 1
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^kA0003840 1 6 15 28 45 66 91 120 153 190 231 276 325 378 435 496 561 630 703 780 861 946 1035 1128 1225
AltPolyRow3 k=0..3 T(3, k) n^kmissing0 -1 -26 -111 -292 -605 -1086 -1771 -2696 -3897 -5410 -7271 -9516 -12181 -15302 -18915 -23056
AltPolyCol2 k=0..n T(n, k) 2^kA0006291 -2 6 -26 150 -1082 9366 -94586 1091670 -14174522 204495126 -3245265146 56183135190 -1053716696762
AltPolyCol3 k=0..n T(n, k) 3^kA2013391 -3 15 -111 1095 -13503 199815 -3449631 68062695 -1510769343 37260156615 -1010843385951
AltPolyDiag k=0..n T(n, k) n^kmissing1 -1 6 -111 4060 -243005 21502866 -2634606331 426748573560 -88276603008249 22701981269322190
RevTriangleT(n, k), 0 ≤ k ≤ nmissing1 1 0 2 1 0 6 6 1 0 24 36 14 1 0 120 240 150 30 1 0 720 1800 1560 540 62 1 0 5040 15120 16800 8400
RevAccsee docsmissing1 1 1 2 3 3 6 12 13 13 24 60 74 75 75 120 360 510 540 541 541 720 2520 4080 4620 4682 4683 4683
RevAccRevsee docsmissing1 0 1 0 1 3 0 1 7 13 0 1 15 51 75 0 1 31 181 421 541 0 1 63 603 2163 3963 4683 0 1 127 1933 10333
RevAntiDiagsee docsmissing1 1 2 0 6 1 24 6 0 120 36 1 720 240 14 0 5040 1800 150 1 40320 15120 1560 30 0 362880 141120 16800
RevDiffx1T(n, k) (k+1)missing1 1 0 2 2 0 6 12 3 0 24 72 42 4 0 120 480 450 120 5 0 720 3600 4680 2160 310 6 0 5040 30240 50400
RevRowSum k=0..n T(n, k)A0006701 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381
RevEvenSum k=0..n T(n, k) even(k)A0321091 1 2 7 38 271 2342 23647 272918 3543631 51123782 811316287 14045783798 263429174191 5320671485222
RevOddSum k=0..n T(n, k) odd(k)missing0 0 1 6 37 270 2341 23646 272917 3543630 51123781 811316286 14045783797 263429174190 5320671485221
RevAltSum k=0..n T(n, k) (-1)^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
RevAbsSum k=0..n | T(n, k) |A0006701 1 3 13 75 541 4683 47293 545835 7087261 102247563 1622632573 28091567595 526858348381
RevDiagSum k=0..n // 2 T(n - k, k)missing1 1 2 7 30 157 974 6991 57030 521341 5280302 58702687 710771670 9311131117 131223143774
RevAccSum k=0..n j=0..k T(n, j)A0056491 2 8 44 308 2612 25988 296564 3816548 54667412 862440068 14857100084 277474957988 5584100659412
RevAccRevSum k=0..n j=0..k T(n, n - j)A1203681 1 4 21 142 1175 11476 129073 1641802 23292459 364530688 6237123365 115806988342 2318774566303
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 6 504 1200 4352400 6501600 31719676464000 3839514683558400 6734455286856081120000
RevRowGcdGcd k=0..n | T(n, k) | > 1A0277601 1 2 6 2 30 2 42 2 30 2 66 2 2730 2 6 2 510 2 798 2 330 2 138 2 2730 2 6 2 870 2 14322 2 510 2 6 2
RevRowMaxMax k=0..n | T(n, k) |A0028691 1 2 6 36 240 1800 16800 191520 2328480 30240000 479001600 8083152000 142702560000 2731586457600
RevColMiddleT(n, n // 2)missing1 1 1 6 14 150 540 8400 40824 834120 5103000 129230640 953029440 28805736960 248619571200
RevCentralET(2 n, n)A2100291 1 14 540 40824 5103000 953029440 248619571200 86355926616960 38528927611574400
RevCentralOT(2 n + 1, n)A2337341 6 150 8400 834120 129230640 28805736960 8734434508800 3457819037312640 1732015476199008000
RevColLeftT(n, 0)A0001421 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200
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)A0003121 1 4 27 256 3125 46656 823543 16777216 387420489 10000000000 285311670611 8916100448256
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA3440531 -1 0 9 -40 -125 3444 -18571 -241872 5796711 -24387220 -1132278191 25132445832 -8850583573
RevTransNat0 k=0..n T(n, k) kmissing0 0 1 8 67 634 6793 81780 1095967 16205198 262283125 4614490792 87715420747 1791916217922
RevTransNat1 k=0..n T(n, k) (k + 1)A1203681 1 4 21 142 1175 11476 129073 1641802 23292459 364530688 6237123365 115806988342 2318774566303
RevTransSqrs k=0..n T(n, k) k^2missing0 0 1 10 101 1126 13917 190002 2848477 46597894 826823669 15826167490 325176345573 7140551306214
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA0041231 2 10 74 730 9002 133210 2299754 45375130 1007179562 24840104410 673895590634 19944372341530
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0006291 -2 6 -26 150 -1082 9366 -94586 1091670 -14174522 204495126 -3245265146 56183135190 -1053716696762
RevDiagRow1T(n + 1, 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
RevDiagRow2T(n + 2, n)A0009182 6 14 30 62 126 254 510 1022 2046 4094 8190 16382 32766 65534 131070 262142 524286 1048574 2097150
RevDiagRow3T(n + 3, n)A0011176 36 150 540 1806 5796 18150 55980 171006 519156 1569750 4733820 14250606 42850116 128746950
RevDiagCol1T(n + 1, 1)A0012860 1 6 36 240 1800 15120 141120 1451520 16329600 199584000 2634508800 37362124800 566658892800
RevDiagCol2T(n + 2, 2)A0379600 1 14 150 1560 16800 191520 2328480 30240000 419126400 6187104000 97037740800 1612798387200
RevDiagCol3T(n + 3, 3)A0379610 1 30 540 8400 126000 1905120 29635200 479001600 8083152000 142702560000 2637143308800
RevPolysee docsmissing1 1 1 2 1 1 6 3 1 1 24 13 4 1 1 120 75 22 5 1 1 720 541 160 33 6 1 1 5040 4683 1456 285 46 7 1 1
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^kA0000272 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 37
RevPolyRow3 k=0..3 T(3, k) n^kA0288726 13 22 33 46 61 78 97 118 141 166 193 222 253 286 321 358 397 438 481 526 573 622 673 726 781 838
RevPolyCol2 k=0..n T(n, k) 2^kA1227041 1 4 22 160 1456 15904 202672 2951680 48361216 880405504 17630351872 385148108800 9114999832576
RevPolyCol3 k=0..n T(n, k) 3^kA2559271 1 5 33 285 3081 40005 606033 10491885 204343641 4422082005 105265315233 2733583519485
RevPolyDiag k=0..n T(n, k) n^kA3316901 1 4 33 456 9445 272448 10386817 503758720 30202999821 2189000524800 188349613075393
 << 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.