CENTRALCYCLE[0] 1
[1] 0, 1
[2] 0, 2, 3
[3] 0, 6, 20, 15
[4] 0, 24, 130, 210, 105
[5] 0, 120, 924, 2380, 2520, 945

      OEIS Similars: A269940, A111999, A259456

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA2699401 0 1 0 2 3 0 6 20 15 0 24 130 210 105 0 120 924 2380 2520 945 0 720 7308 26432 44100 34650 10395 0
StdRevT(n, n - k), 0 ≤ k ≤ nmissing1 1 0 3 2 0 15 20 6 0 105 210 130 24 0 945 2520 2380 924 120 0 10395 34650 44100 26432 7308 720 0
StdAccsee docsmissing1 0 1 0 2 5 0 6 26 41 0 24 154 364 469 0 120 1044 3424 5944 6889 0 720 8028 34460 78560 113210
StdAccRevsee docsmissing1 1 1 3 5 5 15 35 41 41 105 315 445 469 469 945 3465 5845 6769 6889 6889 10395 45045 89145 115577
StdAntiDiagsee docsA1068281 0 0 1 0 2 0 6 3 0 24 20 0 120 130 15 0 720 924 210 0 5040 7308 2380 105 0 40320 64224 26432 2520
StdDiffx1T(n, k) (k+1)missing1 0 2 0 4 9 0 12 60 60 0 48 390 840 525 0 240 2772 9520 12600 5670 0 1440 21924 105728 220500
StdRowSum k=0..n T(n, k)A0321881 1 5 41 469 6889 123605 2620169 64074901 1775623081 54989743445 1882140936521 70552399533589
StdEvenSum k=0..n T(n, k) even(k)missing1 0 3 20 235 3444 61803 1310084 32037451 887811540 27494871723 941070468260 35276199766795
StdOddSum k=0..n T(n, k) odd(k)missing0 1 2 21 234 3445 61802 1310085 32037450 887811541 27494871722 941070468261 35276199766794
StdAbsSum k=0..n | T(n, k) |A0321881 1 5 41 469 6889 123605 2620169 64074901 1775623081 54989743445 1882140936521 70552399533589
StdDiagSum k=0..n // 2 T(n - k, k)A0001661 0 1 2 9 44 265 1854 14833 133496 1334961 14684570 176214841 2290792932 32071101049 481066515734
StdAccSum k=0..n j=0..k T(n, j)missing1 1 7 73 1011 17421 358583 8575169 233499227 7129778357 241209015807 8954112241449 361814361712675
StdAccRevSum k=0..n j=0..k T(n, n - j)missing1 2 13 132 1803 30802 630257 15006352 407249783 12402075534 418667905533 15513719933324
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 6 60 10920 1413720 39840292800 6652505239380000 2048503569859181635200
StdRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
StdRowMaxMax k=0..n | T(n, k) |missing1 1 3 20 210 2520 44100 866250 18858840 520059540 14980405440 486591585480 17856935296200
StdColMiddleT(n, n // 2)missing1 0 2 6 130 924 26432 303660 11098780 177331440 7934927000 162831789120 8637235647040
StdCentralET(2 n, n)missing1 2 130 26432 11098780 7934927000 8637235647040 13306928148113600 27563542664861323120
StdCentralOT(2 n + 1, n)missing0 6 924 303660 177331440 162831789120 216752221445760 395063504843607600 945287743578415036800
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)A0011471 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625
StdBinConv k=0..n C(n, k) T(n, k)missing1 1 7 93 1821 47185 1522375 58808449 2646575953 135989069049 7855656271695 503968974045405
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 1 -1 -27 -51 3505 40655 -828919 -29640527 145577529 27107045415 302955618405 -29149221516195
StdTransNat0 k=0..n T(n, k) kmissing0 1 8 91 1334 23913 506652 12386183 343174882 10626452453 363678162088 13631578996803
StdTransNat1 k=0..n T(n, k) (k + 1)missing1 2 13 132 1803 30802 630257 15006352 407249783 12402075534 418667905533 15513719933324
StdTransSqrs k=0..n T(n, k) k^2missing0 1 14 221 4114 89181 2213910 62017301 1936315234 66696441109 2512886126486 102811622531229
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kmissing1 1 7 79 1237 24817 607519 17560063 585330109 22104345409 932722154743 43492678445551
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0016621 1 -1 -1 13 -47 -73 2447 -16811 -15551 1726511 -18994849 10979677 2983409137 -48421103257
StdDiagRow1T(n + 1, n)A0009060 2 20 210 2520 34650 540540 9459450 183783600 3928374450 91662070500 2319050383650 63246828645000
StdDiagRow2T(n + 2, n)A0009070 6 130 2380 44100 866250 18288270 416215800 10199989800 268438920750 7562120816250 227266937597700
StdDiagRow3T(n + 3, n)A0017840 24 924 26432 705320 18858840 520059540 14980405440 453247114320 14433720701400 483908513388300
StdDiagCol1T(n + 1, 1)A0001421 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
StdDiagCol2T(n + 2, 2)A0002763 20 130 924 7308 64224 623376 6636960 76998240 967524480 13096736640 190060335360 2944310342400
StdDiagCol3T(n + 3, 3)A00048315 210 2380 26432 303660 3678840 47324376 647536032 9418945536 145410580224 2377609752960
StdPolysee docsmissing1 0 1 0 1 1 0 5 2 1 0 41 16 3 1 0 469 212 33 4 1 0 6889 3928 603 56 5 1 0 123605 93536 15417 1304
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^kA0459440 5 16 33 56 85 120 161 208 261 320 385 456 533 616 705 800 901 1008 1121 1240 1365 1496 1633 1776
StdPolyRow3 k=0..3 T(3, k) n^kmissing0 41 212 603 1304 2405 3996 6167 9008 12609 17060 22451 28872 36413 45164 55215 66656 79577 94068
StdPolyCol2 k=0..n T(n, k) 2^kmissing1 2 16 212 3928 93536 2721808 93593216 3713245504 166956801728 8389729444864 465960841779968
StdPolyCol3 k=0..n T(n, k) 3^kmissing1 3 33 603 15417 506691 20351601 966015531 52906036329 3283794968787 227795984943777
StdPolyDiag k=0..n T(n, k) n^kmissing1 1 16 603 42496 4849325 817557840 191243348471 59305251856384 23552891957893329
AltAccsee docsmissing1 0 -1 0 -2 1 0 -6 14 -1 0 -24 106 -104 1 0 -120 804 -1576 944 -1 0 -720 6588 -19844 24256 -10394 1
AltAccRevsee docsmissing1 -1 -1 3 1 1 -15 5 -1 -1 105 -105 25 1 1 -945 1575 -805 119 -1 -1 10395 -24255 19845 -6587 721 1 1
AltAntiDiagsee docsA1068281 0 0 -1 0 -2 0 -6 3 0 -24 20 0 -120 130 -15 0 -720 924 -210 0 -5040 7308 -2380 105 0 -40320 64224
AltDiffx1T(n, k) (k+1)missing1 0 -2 0 -4 9 0 -12 60 -60 0 -48 390 -840 525 0 -240 2772 -9520 12600 -5670 0 -1440 21924 -105728
AltEvenSum k=0..n T(n, k) even(k)missing1 0 3 20 235 3444 61803 1310084 32037451 887811540 27494871723 941070468260 35276199766795
AltOddSum k=0..n T(n, k) odd(k)missing0 -1 -2 -21 -234 -3445 -61802 -1310085 -32037450 -887811541 -27494871722 -941070468261
AltAltSum k=0..n T(n, k) (-1)^kA0321881 1 5 41 469 6889 123605 2620169 64074901 1775623081 54989743445 1882140936521 70552399533589
AltAbsSum k=0..n | T(n, k) |A0321881 1 5 41 469 6889 123605 2620169 64074901 1775623081 54989743445 1882140936521 70552399533589
AltDiagSum k=0..n // 2 T(n - k, k)A0000271 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
AltAccSum k=0..n j=0..k T(n, j)A0703131 -1 -1 7 -21 51 -113 239 -493 1003 -2025 4071 -8165 16355 -32737 65503 -131037 262107 -524249
AltAccRevSum k=0..n j=0..k T(n, n - j)A0003251 -2 5 -12 27 -58 121 -248 503 -1014 2037 -4084 8179 -16370 32753 -65520 131055 -262126 524269
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 6 60 10920 1413720 39840292800 6652505239380000 2048503569859181635200
AltRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
AltRowMaxMax k=0..n | T(n, k) |missing1 1 3 20 210 2520 44100 866250 18858840 520059540 14980405440 486591585480 17856935296200
AltColMiddleT(n, n // 2)missing1 0 -2 -6 130 924 -26432 -303660 11098780 177331440 -7934927000 -162831789120 8637235647040
AltCentralET(2 n, n)missing1 -2 130 -26432 11098780 -7934927000 8637235647040 -13306928148113600 27563542664861323120
AltCentralOT(2 n + 1, n)missing0 -6 924 -303660 177331440 -162831789120 216752221445760 -395063504843607600 945287743578415036800
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)A0011471 -1 3 -15 105 -945 10395 -135135 2027025 -34459425 654729075 -13749310575 316234143225
AltBinConv k=0..n C(n, k) T(n, k)missing1 -1 -1 27 -51 -3505 40655 828919 -29640527 -145577529 27107045415 -302955618405 -29149221516195
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 7 -93 1821 -47185 1522375 -58808449 2646575953 -135989069049 7855656271695 -503968974045405
AltTransNat0 k=0..n T(n, k) kA0002950 -1 4 -11 26 -57 120 -247 502 -1013 2036 -4083 8178 -16369 32752 -65519 131054 -262125 524268
AltTransNat1 k=0..n T(n, k) (k + 1)A0003251 -2 5 -12 27 -58 121 -248 503 -1014 2037 -4084 8179 -16370 32753 -65520 131055 -262126 524269
AltTransSqrs k=0..n T(n, k) k^2missing0 -1 10 -61 286 -1149 4194 -14389 47374 -151669 476290 -1475709 4529214 -13808461 41900098
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kA0016621 -1 -1 1 13 47 -73 -2447 -16811 15551 1726511 18994849 10979677 -2983409137 -48421103257
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 -1 7 -79 1237 -24817 607519 -17560063 585330109 -22104345409 932722154743 -43492678445551
AltDiagRow1T(n + 1, n)A0009060 -2 20 -210 2520 -34650 540540 -9459450 183783600 -3928374450 91662070500 -2319050383650
AltDiagRow2T(n + 2, n)A0009070 -6 130 -2380 44100 -866250 18288270 -416215800 10199989800 -268438920750 7562120816250
AltDiagRow3T(n + 3, n)A0017840 -24 924 -26432 705320 -18858840 520059540 -14980405440 453247114320 -14433720701400
AltDiagCol1T(n + 1, 1)A000142-1 -2 -6 -24 -120 -720 -5040 -40320 -362880 -3628800 -39916800 -479001600 -6227020800 -87178291200
AltDiagCol2T(n + 2, 2)A0002763 20 130 924 7308 64224 623376 6636960 76998240 967524480 13096736640 190060335360 2944310342400
AltDiagCol3T(n + 3, 3)A000483-15 -210 -2380 -26432 -303660 -3678840 -47324376 -647536032 -9418945536 -145410580224
AltPolysee docsmissing1 0 1 0 -1 1 0 1 -2 1 0 -1 8 -3 1 0 1 -52 21 -4 1 0 -1 472 -243 40 -5 1 0 1 -5504 3933 -664 65 -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^kA0005670 1 8 21 40 65 96 133 176 225 280 341 408 481 560 645 736 833 936 1045 1160 1281 1408 1541 1680
AltPolyRow3 k=0..3 T(3, k) n^kmissing0 -1 -52 -243 -664 -1405 -2556 -4207 -6448 -9369 -13060 -17611 -23112 -29653 -37324 -46215 -56416
AltPolyCol2 k=0..n T(n, k) 2^kA0063511 -2 8 -52 472 -5504 78416 -1320064 25637824 -564275648 13879795712 -377332365568 11234698041088
AltPolyCol3 k=0..n T(n, k) 3^kA0585621 -3 21 -243 3933 -81819 2080053 -62490339 2166106509 -85092601707 3735939709989 -181287330220467
AltPolyDiag k=0..n T(n, k) n^kmissing1 -1 8 -243 15424 -1653125 267253776 -60662126959 18389742168064 -7175239308404649
RevTriangleT(n, k), 0 ≤ k ≤ nmissing1 1 0 3 2 0 15 20 6 0 105 210 130 24 0 945 2520 2380 924 120 0 10395 34650 44100 26432 7308 720 0
RevAccsee docsmissing1 1 1 3 5 5 15 35 41 41 105 315 445 469 469 945 3465 5845 6769 6889 6889 10395 45045 89145 115577
RevAccRevsee docsmissing1 0 1 0 2 5 0 6 26 41 0 24 154 364 469 0 120 1044 3424 5944 6889 0 720 8028 34460 78560 113210
RevAntiDiagsee docsmissing1 1 3 0 15 2 105 20 0 945 210 6 10395 2520 130 0 135135 34650 2380 24 2027025 540540 44100 924 0
RevDiffx1T(n, k) (k+1)missing1 1 0 3 4 0 15 40 18 0 105 420 390 96 0 945 5040 7140 3696 600 0 10395 69300 132300 105728 36540
RevRowSum k=0..n T(n, k)A0321881 1 5 41 469 6889 123605 2620169 64074901 1775623081 54989743445 1882140936521 70552399533589
RevEvenSum k=0..n T(n, k) even(k)missing1 1 3 21 235 3445 61803 1310085 32037451 887811541 27494871723 941070468261 35276199766795
RevOddSum k=0..n T(n, k) odd(k)missing0 0 2 20 234 3444 61802 1310084 32037450 887811540 27494871722 941070468260 35276199766794
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) |A0321881 1 5 41 469 6889 123605 2620169 64074901 1775623081 54989743445 1882140936521 70552399533589
RevDiagSum k=0..n // 2 T(n - k, k)missing1 1 3 17 125 1161 13045 172189 2612589 44811677 857513573 18113064045 418627426069 10508716423405
RevAccSum k=0..n j=0..k T(n, j)missing1 2 13 132 1803 30802 630257 15006352 407249783 12402075534 418667905533 15513719933324
RevAccRevSum k=0..n j=0..k T(n, n - j)missing1 1 7 73 1011 17421 358583 8575169 233499227 7129778357 241209015807 8954112241449 361814361712675
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 6 60 10920 1413720 39840292800 6652505239380000 2048503569859181635200
RevRowGcdGcd k=0..n | T(n, k) | > 1A0000121 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
RevRowMaxMax k=0..n | T(n, k) |missing1 1 3 20 210 2520 44100 866250 18858840 520059540 14980405440 486591585480 17856935296200
RevColMiddleT(n, n // 2)missing1 1 2 20 130 2380 26432 705320 11098780 389449060 7934927000 345240896000 8637235647040
RevCentralET(2 n, n)missing1 2 130 26432 11098780 7934927000 8637235647040 13306928148113600 27563542664861323120
RevCentralOT(2 n + 1, n)missing1 20 2380 705320 389449060 345240896000 448594185959920 803351393628623840 1896599794387175878000
RevColLeftT(n, 0)A0011471 1 3 15 105 945 10395 135135 2027025 34459425 654729075 13749310575 316234143225 7905853580625
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)missing1 1 7 93 1821 47185 1522375 58808449 2646575953 135989069049 7855656271695 503968974045405
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 -1 27 -51 -3505 40655 828919 -29640527 -145577529 27107045415 -302955618405 -29149221516195
RevTransNat0 k=0..n T(n, k) kmissing0 0 2 32 542 10532 234978 5955000 169424326 5354155276 186219272362 7071971304928 291261962179086
RevTransNat1 k=0..n T(n, k) (k + 1)missing1 1 7 73 1011 17421 358583 8575169 233499227 7129778357 241209015807 8954112241449 361814361712675
RevTransSqrs k=0..n T(n, k) k^2missing0 0 2 44 946 22276 583866 16999020 546310786 19245766516 738297229226 30655937920604
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kmissing1 2 16 212 3928 93536 2721808 93593216 3713245504 166956801728 8389729444864 465960841779968
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0063511 -2 8 -52 472 -5504 78416 -1320064 25637824 -564275648 13879795712 -377332365568 11234698041088
RevDiagRow1T(n + 1, n)A0001421 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
RevDiagRow2T(n + 2, n)A0002763 20 130 924 7308 64224 623376 6636960 76998240 967524480 13096736640 190060335360 2944310342400
RevDiagRow3T(n + 3, n)A00048315 210 2380 26432 303660 3678840 47324376 647536032 9418945536 145410580224 2377609752960
RevDiagCol1T(n + 1, 1)A0009060 2 20 210 2520 34650 540540 9459450 183783600 3928374450 91662070500 2319050383650 63246828645000
RevDiagCol2T(n + 2, 2)A0009070 6 130 2380 44100 866250 18288270 416215800 10199989800 268438920750 7562120816250 227266937597700
RevDiagCol3T(n + 3, 3)A0017840 24 924 26432 705320 18858840 520059540 14980405440 453247114320 14433720701400 483908513388300
RevPolysee docsmissing1 1 1 3 1 1 15 5 1 1 105 41 7 1 1 945 469 79 9 1 1 10395 6889 1237 129 11 1 1 135135 123605 24817
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^kA0054083 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^kA23932515 41 79 129 191 265 351 449 559 681 815 961 1119 1289 1471 1665 1871 2089 2319 2561 2815 3081 3359
RevPolyCol2 k=0..n T(n, k) 2^kmissing1 1 7 79 1237 24817 607519 17560063 585330109 22104345409 932722154743 43492678445551
RevPolyCol3 k=0..n T(n, k) 3^kmissing1 1 9 129 2553 64593 1991817 72473697 3039768729 144405631089 7663786510761 449399632734081
RevPolyDiag k=0..n T(n, k) n^kmissing1 1 7 129 4561 263545 22585095 2689741313 424884156769 85956226636041 21670469260893575
 << 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.