NARAYANA[0] 1
[1] 0, 1
[2] 0, 1, 1
[3] 0, 1, 3, 1
[4] 0, 1, 6, 6, 1
[5] 0, 1, 10, 20, 10, 1

      OEIS Similars: A090181, A001263, A131198

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA0901811 0 1 0 1 1 0 1 3 1 0 1 6 6 1 0 1 10 20 10 1 0 1 15 50 50 15 1 0 1 21 105 175 105 21 1 0 1 28 196
StdRevT(n, n - k), 0 ≤ k ≤ nA0901811 1 0 1 1 0 1 3 1 0 1 6 6 1 0 1 10 20 10 1 0 1 15 50 50 15 1 0 1 21 105 175 105 21 1 0 1 28 196 490
StdInvT-1(n, k), 0 ≤ k ≤ nmissing1 0 1 0 -1 1 0 2 -3 1 0 -7 12 -6 1 0 39 -70 40 -10 1 0 -321 585 -350 100 -15 1 0 3681 -6741 4095
StdRevInvT-1(n, n - k), 0 ≤ k ≤ nmissing1 1 0 1 -1 0 1 -3 2 0 1 -6 12 -7 0 1 -10 40 -70 39 0 1 -15 100 -350 585 -321 0 1 -21 210 -1225 4095
StdAccsee docsA3497401 0 1 0 1 2 0 1 4 5 0 1 7 13 14 0 1 11 31 41 42 0 1 16 66 116 131 132 0 1 22 127 302 407 428 429 0
StdAccRevsee docsmissing1 1 1 1 2 2 1 4 5 5 1 7 13 14 14 1 11 31 41 42 42 1 16 66 116 131 132 132 1 22 127 302 407 428 429
StdAntiDiagsee docsmissing1 0 0 1 0 1 0 1 1 0 1 3 0 1 6 1 0 1 10 6 0 1 15 20 1 0 1 21 50 10 0 1 28 105 50 1 0 1 36 196 175 15
StdDiffx1T(n, k) (k+1)missing1 0 2 0 2 3 0 2 9 4 0 2 18 24 5 0 2 30 80 50 6 0 2 45 200 250 90 7 0 2 63 420 875 630 147 8 0 2 84
StdRowSum k=0..n T(n, k)A0001081 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790
StdEvenSum k=0..n T(n, k) even(k)A0716881 0 1 3 7 20 66 217 715 2424 8398 29414 104006 371384 1337220 4847637 17678835 64821680 238819350
StdOddSum k=0..n T(n, k) odd(k)A0716840 1 1 2 7 22 66 212 715 2438 8398 29372 104006 371516 1337220 4847208 17678835 64823110 238819350
StdAltSum k=0..n T(n, k) (-1)^kA1261201 -1 0 1 0 -2 0 5 0 -14 0 42 0 -132 0 429 0 -1430 0 4862 0 -16796 0 58786 0 -208012 0 742900 0
StdAbsSum k=0..n | T(n, k) |A0001081 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790
StdDiagSum k=0..n // 2 T(n - k, k)A0041481 0 1 1 2 4 8 17 37 82 185 423 978 2283 5373 12735 30372 72832 175502 424748 1032004 2516347
StdAccSum k=0..n j=0..k T(n, j)A0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
StdAccRevSum k=0..n j=0..k T(n, n - j)A1891761 2 5 15 49 168 594 2145 7865 29172 109174 411502 1560090 5943200 22732740 87253605 335897865
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 1 3 6 20 150 525 980 7056 52920 485100 4573800 3397680 5153148 135270135 1803601800 27254427200
StdRowGcdGcd k=0..n | T(n, k) | > 1missing1 1 1 3 6 10 5 7 14 12 9 11 11 13 13 1 2 68 17 19 19 1 1 23 23 5 25 3 9 29 29 31 62 4 1 1 1 37 37 1
StdRowMaxMax k=0..n | T(n, k) |A0055581 1 1 3 6 20 50 175 490 1764 5292 19404 60984 226512 736164 2760615 9202050 34763300 118195220
StdColMiddleT(n, n // 2)missing1 0 1 1 6 10 50 105 490 1176 5292 13860 60984 169884 736164 2147145 9202050 27810640 118195220
StdCentralET(2 n, n)A1255581 1 6 50 490 5292 60984 736164 9202050 118195220 1551580888 20734762776 281248448936 3863302870000
StdCentralOT(2 n + 1, n)A0467150 1 10 105 1176 13860 169884 2147145 27810640 367479684 4936848280 67255063876 927192688800
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)missing1 1 3 13 65 356 2072 12601 79221 511174 3368090 22577160 153534680 1056945280 7352977504
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 1 -1 -5 9 56 -120 -825 1925 14014 -34398 -259896 659736 5116320 -13302432 -105172353 278397405
StdTransNat0 k=0..n T(n, k) kA0017000 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
StdTransNat1 k=0..n T(n, k) (k + 1)A1891761 2 5 15 49 168 594 2145 7865 29172 109174 411502 1560090 5943200 22732740 87253605 335897865
StdTransSqrs k=0..n T(n, k) k^2A1412220 1 5 22 95 406 1722 7260 30459 127270 529958 2200276 9111830 37650172 155266100 639191160
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kA0010031 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0915931 1 -1 -1 5 -3 -21 51 41 -391 407 1927 -6227 -2507 49347 -71109 -236079 966129 9519 -7408497
StdDiagRow1T(n + 1, n)A0002170 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406
StdDiagRow2T(n + 2, n)A0024150 1 6 20 50 105 196 336 540 825 1210 1716 2366 3185 4200 5440 6936 8721 10830 13300 16170 19481
StdDiagRow3T(n + 3, n)A0065420 1 10 50 175 490 1176 2520 4950 9075 15730 26026 41405 63700 95200 138720 197676 276165 379050
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)A0002171 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435
StdDiagCol3T(n + 3, 3)A0024151 6 20 50 105 196 336 540 825 1210 1716 2366 3185 4200 5440 6936 8721 10830 13300 16170 19481 23276
StdPolysee docsmissing1 0 1 0 1 1 0 2 2 1 0 5 6 3 1 0 14 22 12 4 1 0 42 90 57 20 5 1 0 132 394 300 116 30 6 1 0 429 1806
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^kA0023780 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702 756
StdPolyRow3 k=0..3 T(3, k) n^kA0334450 5 22 57 116 205 330 497 712 981 1310 1705 2172 2717 3346 4065 4880 5797 6822 7961 9220 10605
StdPolyCol2 k=0..n T(n, k) 2^kA0063181 2 6 22 90 394 1806 8558 41586 206098 1037718 5293446 27297738 142078746 745387038 3937603038
StdPolyCol3 k=0..n T(n, k) 3^kA0478911 3 12 57 300 1686 9912 60213 374988 2381322 15361896 100389306 663180024 4421490924 29712558576
StdPolyDiag k=0..n T(n, k) n^kmissing1 1 6 57 740 12130 239442 5516133 145043208 4281280686 140046944510 5025026633946 196122756175788
AltTriangleT(n, k), 0 ≤ k ≤ nA0901811 0 -1 0 -1 1 0 -1 3 -1 0 -1 6 -6 1 0 -1 10 -20 10 -1 0 -1 15 -50 50 -15 1 0 -1 21 -105 175 -105 21
AltRevT(n, n - k), 0 ≤ k ≤ nA0901811 -1 0 1 -1 0 -1 3 -1 0 1 -6 6 -1 0 -1 10 -20 10 -1 0 1 -15 50 -50 15 -1 0 -1 21 -105 175 -105 21
AltInvT-1(n, k), 0 ≤ k ≤ nmissing1 0 1 0 1 1 0 -2 -3 1 0 -17 -24 6 1 0 121 170 -40 -10 1 0 2551 3585 -850 -200 15 1 0 -38121 -53571
AltRevInvT-1(n, n - k), 0 ≤ k ≤ nmissing1 1 0 1 1 0 1 -3 -2 0 1 6 -24 -17 0 1 -10 -40 170 121 0 1 15 -200 -850 3585 2551 0 1 -21 -210 2975
AltAccsee docsmissing1 0 -1 0 -1 0 0 -1 2 1 0 -1 5 -1 0 0 -1 9 -11 -1 -2 0 -1 14 -36 14 -1 0 0 -1 20 -85 90 -15 6 5 0 -1
AltAccRevsee docsmissing1 -1 -1 1 0 0 -1 2 1 1 1 -5 1 0 0 -1 9 -11 -1 -2 -2 1 -14 36 -14 1 0 0 -1 20 -85 90 -15 6 5 5 1 -27
AltAntiDiagsee docsmissing1 0 0 -1 0 -1 0 -1 1 0 -1 3 0 -1 6 -1 0 -1 10 -6 0 -1 15 -20 1 0 -1 21 -50 10 0 -1 28 -105 50 -1 0
AltDiffx1T(n, k) (k+1)missing1 0 -2 0 -2 3 0 -2 9 -4 0 -2 18 -24 5 0 -2 30 -80 50 -6 0 -2 45 -200 250 -90 7 0 -2 63 -420 875
AltRowSum k=0..n T(n, k)A1261201 -1 0 1 0 -2 0 5 0 -14 0 42 0 -132 0 429 0 -1430 0 4862 0 -16796 0 58786 0 -208012 0 742900 0
AltEvenSum k=0..n T(n, k) even(k)A0716881 0 1 3 7 20 66 217 715 2424 8398 29414 104006 371384 1337220 4847637 17678835 64821680 238819350
AltOddSum k=0..n T(n, k) odd(k)A0716840 -1 -1 -2 -7 -22 -66 -212 -715 -2438 -8398 -29372 -104006 -371516 -1337220 -4847208 -17678835
AltAltSum k=0..n T(n, k) (-1)^kA0001081 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790
AltAbsSum k=0..n | T(n, k) |A0001081 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790
AltDiagSum k=0..n // 2 T(n - k, k)A1295091 0 -1 -1 0 2 4 3 -5 -20 -29 -1 94 221 191 -327 -1454 -2282 -162 8002 19902 18275 -30505 -143511
AltAccSum k=0..n j=0..k T(n, j)A0014051 -1 -1 2 3 -6 -10 20 35 -70 -126 252 462 -924 -1716 3432 6435 -12870 -24310 48620 92378 -184756
AltAccRevSum k=0..n j=0..k T(n, n - j)missing1 -2 1 3 -3 -8 10 25 -35 -84 126 294 -462 -1056 1716 3861 -6435 -14300 24310 53482 -92378 -201552
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 1 3 6 20 150 525 980 7056 52920 485100 4573800 3397680 5153148 135270135 1803601800 27254427200
AltRowGcdGcd k=0..n | T(n, k) | > 1missing1 1 1 3 6 10 5 7 14 12 9 11 11 13 13 1 2 68 17 19 19 1 1 23 23 5 25 3 9 29 29 31 62 4 1 1 1 37 37 1
AltRowMaxMax k=0..n | T(n, k) |A0055581 1 1 3 6 20 50 175 490 1764 5292 19404 60984 226512 736164 2760615 9202050 34763300 118195220
AltColMiddleT(n, n // 2)missing1 0 -1 -1 6 10 -50 -105 490 1176 -5292 -13860 60984 169884 -736164 -2147145 9202050 27810640
AltCentralET(2 n, n)A1255581 -1 6 -50 490 -5292 60984 -736164 9202050 -118195220 1551580888 -20734762776 281248448936
AltCentralOT(2 n + 1, n)A0467150 -1 10 -105 1176 -13860 169884 -2147145 27810640 -367479684 4936848280 -67255063876 927192688800
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 -1 5 9 -56 -120 825 1925 -14014 -34398 259896 659736 -5116320 -13302432 105172353 278397405
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 3 -13 65 -356 2072 -12601 79221 -511174 3368090 -22577160 153534680 -1056945280 7352977504
AltTransNat0 k=0..n T(n, k) kA0014050 -1 1 2 -3 -6 10 20 -35 -70 126 252 -462 -924 1716 3432 -6435 -12870 24310 48620 -92378 -184756
AltTransNat1 k=0..n T(n, k) (k + 1)missing1 -2 1 3 -3 -8 10 25 -35 -84 126 294 -462 -1056 1716 3861 -6435 -14300 24310 53482 -92378 -201552
AltTransSqrs k=0..n T(n, k) k^2missing0 -1 3 2 -15 -6 70 20 -315 -70 1386 252 -6006 -924 25740 3432 -109395 -12870 461890 48620 -1939938
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kA0915931 -1 -1 1 5 3 -21 -51 41 391 407 -1927 -6227 2507 49347 71109 -236079 -966129 9519 7408497 13685205
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0010031 -1 3 -11 45 -197 903 -4279 20793 -103049 518859 -2646723 13648869 -71039373 372693519 -1968801519
AltDiagRow1T(n + 1, n)A0002170 -1 3 -6 10 -15 21 -28 36 -45 55 -66 78 -91 105 -120 136 -153 171 -190 210 -231 253 -276 300 -325
AltDiagRow2T(n + 2, n)A0024150 -1 6 -20 50 -105 196 -336 540 -825 1210 -1716 2366 -3185 4200 -5440 6936 -8721 10830 -13300 16170
AltDiagRow3T(n + 3, n)A0065420 -1 10 -50 175 -490 1176 -2520 4950 -9075 15730 -26026 41405 -63700 95200 -138720 197676 -276165
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)A0002171 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435
AltDiagCol3T(n + 3, 3)A002415-1 -6 -20 -50 -105 -196 -336 -540 -825 -1210 -1716 -2366 -3185 -4200 -5440 -6936 -8721 -10830
AltPolysee docsmissing1 0 1 0 -1 1 0 0 -2 1 0 1 2 -3 1 0 0 2 6 -4 1 0 -2 -10 -3 12 -5 1 0 0 6 -30 -20 20 -6 1 0 5 42 114
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^kA0023780 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702
AltPolyRow3 k=0..3 T(3, k) n^kA3187650 1 2 -3 -20 -55 -114 -203 -328 -495 -710 -979 -1308 -1703 -2170 -2715 -3344 -4063 -4878 -5795
AltPolyCol2 k=0..n T(n, k) 2^kA1526811 -2 2 2 -10 6 42 -102 -82 782 -814 -3854 12454 5014 -98694 142218 472158 -1932258 -19038 14816994
AltPolyCol3 k=0..n T(n, k) 3^kmissing1 -3 6 -3 -30 114 -84 -867 3786 -3162 -33132 153906 -136812 -1446204 6957528 -6420387 -68260134
AltPolyDiag k=0..n T(n, k) n^kmissing1 -1 2 -3 -36 870 -15450 267533 -4710664 83469762 -1412535510 19138692562 9041033364
RevTriangleT(n, k), 0 ≤ k ≤ nA0901811 1 0 1 1 0 1 3 1 0 1 6 6 1 0 1 10 20 10 1 0 1 15 50 50 15 1 0 1 21 105 175 105 21 1 0 1 28 196 490
RevInvRev(T(n, n - k))-1, 0 ≤ k ≤ nmissing1 0 1 0 -1 1 0 2 -3 1 0 -7 12 -6 1 0 39 -70 40 -10 1 0 -321 585 -350 100 -15 1 0 3681 -6741 4095
RevAccsee docsmissing1 1 1 1 2 2 1 4 5 5 1 7 13 14 14 1 11 31 41 42 42 1 16 66 116 131 132 132 1 22 127 302 407 428 429
RevAccRevsee docsA3497401 0 1 0 1 2 0 1 4 5 0 1 7 13 14 0 1 11 31 41 42 0 1 16 66 116 131 132 0 1 22 127 302 407 428 429 0
RevAntiDiagsee docsmissing1 1 1 0 1 1 1 3 0 1 6 1 1 10 6 0 1 15 20 1 1 21 50 10 0 1 28 105 50 1 1 36 196 175 15 0 1 45 336
RevDiffx1T(n, k) (k+1)A3672701 1 0 1 2 0 1 6 3 0 1 12 18 4 0 1 20 60 40 5 0 1 30 150 200 75 6 0 1 42 315 700 525 126 7 0 1 56
RevRowSum k=0..n T(n, k)A0001081 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790
RevEvenSum k=0..n T(n, k) even(k)A0716841 1 1 2 7 22 66 212 715 2438 8398 29372 104006 371516 1337220 4847208 17678835 64823110 238819350
RevOddSum k=0..n T(n, k) odd(k)A0716880 0 1 3 7 20 66 217 715 2424 8398 29414 104006 371384 1337220 4847637 17678835 64821680 238819350
RevAltSum k=0..n T(n, k) (-1)^kA1261201 1 0 -1 0 2 0 -5 0 14 0 -42 0 132 0 -429 0 1430 0 -4862 0 16796 0 -58786 0 208012 0 -742900 0
RevAbsSum k=0..n | T(n, k) |A0001081 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790
RevDiagSum k=0..n // 2 T(n - k, k)A0041481 1 1 2 4 8 17 37 82 185 423 978 2283 5373 12735 30372 72832 175502 424748 1032004 2516347 6155441
RevAccSum k=0..n j=0..k T(n, j)A1891761 2 5 15 49 168 594 2145 7865 29172 109174 411502 1560090 5943200 22732740 87253605 335897865
RevAccRevSum k=0..n j=0..k T(n, n - j)A0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 1 3 6 20 150 525 980 7056 52920 485100 4573800 3397680 5153148 135270135 1803601800 27254427200
RevRowGcdGcd k=0..n | T(n, k) | > 1missing1 1 1 3 6 10 5 7 14 12 9 11 11 13 13 1 2 68 17 19 19 1 1 23 23 5 25 3 9 29 29 31 62 4 1 1 1 37 37 1
RevRowMaxMax k=0..n | T(n, k) |A0055581 1 1 3 6 20 50 175 490 1764 5292 19404 60984 226512 736164 2760615 9202050 34763300 118195220
RevColMiddleT(n, n // 2)A0055581 1 1 3 6 20 50 175 490 1764 5292 19404 60984 226512 736164 2760615 9202050 34763300 118195220
RevCentralET(2 n, n)A1255581 1 6 50 490 5292 60984 736164 9202050 118195220 1551580888 20734762776 281248448936 3863302870000
RevCentralOT(2 n + 1, n)A0008911 3 20 175 1764 19404 226512 2760615 34763300 449141836 5924217936 79483257308 1081724803600
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)missing1 1 3 13 65 356 2072 12601 79221 511174 3368090 22577160 153534680 1056945280 7352977504
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 -1 5 9 -56 -120 825 1925 -14014 -34398 259896 659736 -5116320 -13302432 105172353 278397405
RevTransNat0 k=0..n T(n, k) kA0020540 0 1 5 21 84 330 1287 5005 19448 75582 293930 1144066 4457400 17383860 67863915 265182525
RevTransNat1 k=0..n T(n, k) (k + 1)A0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
RevTransSqrs k=0..n T(n, k) k^2A0342670 0 1 7 39 196 930 4257 19019 83512 361998 1553630 6615686 27992472 117823940 493768485 2061580275
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA0063181 2 6 22 90 394 1806 8558 41586 206098 1037718 5293446 27297738 142078746 745387038 3937603038
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA1526811 -2 2 2 -10 6 42 -102 -82 782 -814 -3854 12454 5014 -98694 142218 472158 -1932258 -19038 14816994
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)A0002171 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435
RevDiagRow3T(n + 3, n)A0024151 6 20 50 105 196 336 540 825 1210 1716 2366 3185 4200 5440 6936 8721 10830 13300 16170 19481 23276
RevDiagCol1T(n + 1, 1)A0002170 1 3 6 10 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406
RevDiagCol2T(n + 2, 2)A0024150 1 6 20 50 105 196 336 540 825 1210 1716 2366 3185 4200 5440 6936 8721 10830 13300 16170 19481
RevDiagCol3T(n + 3, 3)A0065420 1 10 50 175 490 1176 2520 4950 9075 15730 26026 41405 63700 95200 138720 197676 276165 379050
RevPolysee docsA0085501 1 1 1 1 1 1 2 1 1 1 5 3 1 1 1 14 11 4 1 1 1 42 45 19 5 1 1 1 132 197 100 29 6 1 1 1 429 903 562
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^kA0000271 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
RevPolyRow3 k=0..3 T(3, k) n^kA0283871 5 11 19 29 41 55 71 89 109 131 155 181 209 239 271 305 341 379 419 461 505 551 599 649 701 755
RevPolyCol2 k=0..n T(n, k) 2^kA0010031 1 3 11 45 197 903 4279 20793 103049 518859 2646723 13648869 71039373 372693519 1968801519
RevPolyCol3 k=0..n T(n, k) 3^kA0075641 1 4 19 100 562 3304 20071 124996 793774 5120632 33463102 221060008 1473830308 9904186192
RevPolyDiag k=0..n T(n, k) n^kA2423691 1 3 19 185 2426 39907 788019 18130401 475697854 14004694451 456820603086 16343563014649
InvTriangleT(n, k), 0 ≤ k ≤ nmissing1 0 1 0 -1 1 0 2 -3 1 0 -7 12 -6 1 0 39 -70 40 -10 1 0 -321 585 -350 100 -15 1 0 3681 -6741 4095
InvRevT(n, n - k), 0 ≤ k ≤ nmissing1 1 0 1 -1 0 1 -3 2 0 1 -6 12 -7 0 1 -10 40 -70 39 0 1 -15 100 -350 585 -321 0 1 -21 210 -1225 4095
InvRevInvT-1(n, n - k), 0 ≤ k ≤ nA0901811 1 0 1 1 0 1 3 1 0 1 6 6 1 0 1 10 20 10 1 0 1 15 50 50 15 1 0 1 21 105 175 105 21 1 0 1 28 196 490
InvAccsee docsmissing1 0 1 0 -1 0 0 2 -1 0 0 -7 5 -1 0 0 39 -31 9 -1 0 0 -321 264 -86 14 -1 0 0 3681 -3060 1035 -190 20
InvAccRevsee docsmissing1 1 1 1 0 0 1 -2 0 0 1 -5 7 0 0 1 -9 31 -39 0 0 1 -14 86 -264 321 0 0 1 -20 190 -1035 3060 -3681 0
InvAntiDiagsee docsmissing1 0 0 1 0 -1 0 2 1 0 -7 -3 0 39 12 1 0 -321 -70 -6 0 3681 585 40 1 0 -56197 -6741 -350 -10 0
InvDiffx1T(n, k) (k+1)missing1 0 2 0 -2 3 0 4 -9 4 0 -14 36 -24 5 0 78 -210 160 -50 6 0 -642 1755 -1400 500 -90 7 0 7362 -20223
InvRowSum k=0..n T(n, k)A0195901 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
InvEvenSum k=0..n T(n, k) even(k)missing1 0 1 -3 13 -80 686 -7987 122571 -2408856 59099284 -1771445324 63708974748 -2707745497184
InvOddSum k=0..n T(n, k) odd(k)missing0 1 -1 3 -13 80 -686 7987 -122571 2408856 -59099284 1771445324 -63708974748 2707745497184
InvAltSum k=0..n T(n, k) (-1)^kA1033671 -1 2 -6 26 -160 1372 -15974 245142 -4817712 118198568 -3542890648 127417949496 -5415490994368
InvAbsSum k=0..n | T(n, k) |A1033671 1 2 6 26 160 1372 15974 245142 4817712 118198568 3542890648 127417949496 5415490994368
InvDiagSum k=0..n // 2 T(n - k, k)missing1 0 1 -1 3 -10 52 -397 4307 -63298 1209835 -29123735 861135230 -30656964145 1292847813913
InvAccSum k=0..n j=0..k T(n, j)A1314901 1 -1 1 -3 16 -130 1485 -22645 444136 -10889676 326345460 -11736144420 498798542880
InvAccRevSum k=0..n j=0..k T(n, n - j)A1314901 2 1 -1 3 -16 130 -1485 22645 -444136 10889676 -326345460 11736144420 -498798542880 24732729791484
InvRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 1 6 84 10920 8763300 12544663950 3947845887989640 10446672932559900874656
InvRowGcdGcd 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
InvRowMaxMax k=0..n | T(n, k) |A1033661 1 1 3 12 70 585 6741 103068 2023092 49615695 1487006785 53477384268 2272859942574 112699083156751
InvColMiddleT(n, n // 2)missing1 0 -1 2 12 -70 -350 4095 19110 -377496 -1698732 51018660 224482104 -9546971148 -41370208308
InvCentralET(2 n, n)missing1 -1 12 -350 19110 -1698732 224482104 -41370208308 10145913470550 -3195583528992140
InvCentralOT(2 n + 1, n)missing0 2 -70 4095 -377496 51018660 -9546971148 2367379809795 -751902006821680 297755337453806232
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)missing1 1 -1 -2 21 -154 1260 -11080 69405 1420552 -118046628 6282922086 -325932371226 17821090063128
InvInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 1 3 16 125 1346 19292 358086 8399757 243595792 8566209740 359216007162 17706825237686
InvTransNat0 k=0..n T(n, k) kA1314900 1 1 -1 3 -16 130 -1485 22645 -444136 10889676 -326345460 11736144420 -498798542880 24732729791484
InvTransNat1 k=0..n T(n, k) (k + 1)A1314901 2 1 -1 3 -16 130 -1485 22645 -444136 10889676 -326345460 11736144420 -498798542880 24732729791484
InvTransSqrs k=0..n T(n, k) k^2A1314900 1 3 -1 3 -16 130 -1485 22645 -444136 10889676 -326345460 11736144420 -498798542880 24732729791484
InvPosHalf k=0..n 2^n T(n, k) (1/2)^kmissing1 1 -1 3 -19 205 -3341 76391 -2330343 91416249 -4482922489 268693075915 -19325695148475
InvNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 1 3 15 117 1365 22863 527499 16137705 633619401 31080114747 1863000052551 133999138524573
InvDiagRow1T(n + 1, n)A0002170 -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253
InvDiagRow2T(n + 2, n)A0089110 2 12 40 100 210 392 672 1080 1650 2420 3432 4732 6370 8400 10880 13872 17442 21660 26600 32340
InvDiagRow3T(n + 3, n)missing0 -7 -70 -350 -1225 -3430 -8232 -17640 -34650 -63525 -110110 -182182 -289835 -445900 -666400
InvDiagCol1T(n + 1, 1)A1033651 -1 2 -7 39 -321 3681 -56197 1102571 -27036487 810263398 -29139230033 1238451463261
InvDiagCol2T(n + 2, 2)A1033661 -3 12 -70 585 -6741 103068 -2023092 49615695 -1487006785 53477384268 -2272859942574
InvDiagCol3T(n + 3, 3)missing1 -6 40 -350 4095 -62916 1236816 -30346380 909621075 -32714149270 1390411990968 -68943418258078
InvPolysee docsmissing1 0 1 0 1 1 0 0 2 1 0 0 2 3 1 0 0 0 6 4 1 0 0 2 6 12 5 1 0 0 -10 6 24 20 6 1 0 0 82 0 36 60 30 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^kA0023780 0 2 6 12 20 30 42 56 72 90 110 132 156 182 210 240 272 306 342 380 420 462 506 552 600 650 702
InvPolyRow3 k=0..3 T(3, k) n^kA0075310 0 0 6 24 60 120 210 336 504 720 990 1320 1716 2184 2730 3360 4080 4896 5814 6840 7980 9240 10626
InvPolyCol2 k=0..n T(n, k) 2^kmissing1 2 2 0 2 -10 82 -938 14310 -280698 6882638 -206263552 7417743918 -315262276030 15632160820694
InvPolyCol3 k=0..n T(n, k) 3^kmissing1 3 6 6 6 0 36 -378 5802 -113808 2790744 -83636520 3007792200 -127834699200 6338638537848
InvPolyDiag k=0..n T(n, k) n^kmissing1 1 2 6 36 320 3150 41202 631512 10346688 220824630 4468105400 113821871988 3261960374400
Inv:RevTriangleT(n, k), 0 ≤ k ≤ nmissing1 1 0 1 -1 0 1 -3 2 0 1 -6 12 -7 0 1 -10 40 -70 39 0 1 -15 100 -350 585 -321 0 1 -21 210 -1225 4095
Inv:RevRevT(n, n - k), 0 ≤ k ≤ nmissing1 0 1 0 -1 1 0 2 -3 1 0 -7 12 -6 1 0 39 -70 40 -10 1 0 -321 585 -350 100 -15 1 0 3681 -6741 4095
Inv:RevInvRev(T(n, n - k))-1, 0 ≤ k ≤ nA0901811 0 1 0 1 1 0 1 3 1 0 1 6 6 1 0 1 10 20 10 1 0 1 15 50 50 15 1 0 1 21 105 175 105 21 1 0 1 28 196
Inv:RevAccsee docsmissing1 1 1 1 0 0 1 -2 0 0 1 -5 7 0 0 1 -9 31 -39 0 0 1 -14 86 -264 321 0 0 1 -20 190 -1035 3060 -3681 0
Inv:RevAccRevsee docsmissing1 0 1 0 -1 0 0 2 -1 0 0 -7 5 -1 0 0 39 -31 9 -1 0 0 -321 264 -86 14 -1 0 0 3681 -3060 1035 -190 20
Inv:RevAntiDiagsee docsmissing1 1 1 0 1 -1 1 -3 0 1 -6 2 1 -10 12 0 1 -15 40 -7 1 -21 100 -70 0 1 -28 210 -350 39 1 -36 392 -1225
Inv:RevDiffx1T(n, k) (k+1)missing1 1 0 1 -2 0 1 -6 6 0 1 -12 36 -28 0 1 -20 120 -280 195 0 1 -30 300 -1400 2925 -1926 0 1 -42 630
Inv:RevRowSum k=0..n T(n, k)A0195901 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
Inv:RevEvenSum k=0..n T(n, k) even(k)missing1 1 1 3 13 80 686 7987 122571 2408856 59099284 1771445324 63708974748 2707745497184 134263189722052
Inv:RevOddSum k=0..n T(n, k) odd(k)missing0 0 -1 -3 -13 -80 -686 -7987 -122571 -2408856 -59099284 -1771445324 -63708974748 -2707745497184
Inv:RevAltSum k=0..n T(n, k) (-1)^kA1033671 1 2 6 26 160 1372 15974 245142 4817712 118198568 3542890648 127417949496 5415490994368
Inv:RevAbsSum k=0..n | T(n, k) |A1033671 1 2 6 26 160 1372 15974 245142 4817712 118198568 3542890648 127417949496 5415490994368
Inv:RevDiagSum k=0..n // 2 T(n - k, k)missing1 1 1 0 -2 -3 3 19 10 -128 -283 972 5163 -6494 -100347 -37756 2192992 4783671 -53309108 -247204964
Inv:RevAccSum k=0..n j=0..k T(n, j)A1314901 2 1 -1 3 -16 130 -1485 22645 -444136 10889676 -326345460 11736144420 -498798542880 24732729791484
Inv:RevAccRevSum k=0..n j=0..k T(n, n - j)A1314901 1 -1 1 -3 16 -130 1485 -22645 444136 -10889676 326345460 -11736144420 498798542880
Inv:RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 1 6 84 10920 8763300 12544663950 3947845887989640 10446672932559900874656
Inv: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
Inv:RevRowMaxMax k=0..n | T(n, k) |A1033661 1 1 3 12 70 585 6741 103068 2023092 49615695 1487006785 53477384268 2272859942574 112699083156751
Inv:RevColMiddleT(n, n // 2)missing1 1 -1 -3 12 40 -350 -1225 19110 68796 -1698732 -6228684 224482104 833790672 -41370208308
Inv:RevCentralET(2 n, n)missing1 -1 12 -350 19110 -1698732 224482104 -41370208308 10145913470550 -3195583528992140
Inv:RevCentralOT(2 n + 1, n)missing1 -3 40 -1225 68796 -6228684 833790672 -155138281155 38329006444300 -12143217410170132
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)missing1 1 -1 -2 21 -154 1260 -11080 69405 1420552 -118046628 6282922086 -325932371226 17821090063128
Inv:RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 3 -16 125 -1346 19292 -358086 8399757 -243595792 8566209740 -359216007162 17706825237686
Inv:RevTransNat0 k=0..n T(n, k) kA1314900 0 -1 1 -3 16 -130 1485 -22645 444136 -10889676 326345460 -11736144420 498798542880
Inv:RevTransNat1 k=0..n T(n, k) (k + 1)A1314901 1 -1 1 -3 16 -130 1485 -22645 444136 -10889676 326345460 -11736144420 498798542880
Inv:RevTransSqrs k=0..n T(n, k) k^2missing0 0 -1 5 -21 144 -1430 19305 -339675 7550312 -206903844 6853254660 -269931321660 12469963572000
Inv:RevPosHalf k=0..n 2^n T(n, k) (1/2)^kmissing1 2 2 0 2 -10 82 -938 14310 -280698 6882638 -206263552 7417743918 -315262276030 15632160820694
Inv:RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 -2 6 -24 126 -870 7926 -94878 1472442 -29056038 713851434 -21406520520 769978976850
Inv:RevDiagRow1T(n + 1, n)A1033651 -1 2 -7 39 -321 3681 -56197 1102571 -27036487 810263398 -29139230033 1238451463261
Inv:RevDiagRow2T(n + 2, n)A1033661 -3 12 -70 585 -6741 103068 -2023092 49615695 -1487006785 53477384268 -2272859942574
Inv:RevDiagRow3T(n + 3, n)missing1 -6 40 -350 4095 -62916 1236816 -30346380 909621075 -32714149270 1390411990968 -68943418258078
Inv:RevDiagCol1T(n + 1, 1)A0002170 -1 -3 -6 -10 -15 -21 -28 -36 -45 -55 -66 -78 -91 -105 -120 -136 -153 -171 -190 -210 -231 -253
Inv:RevDiagCol2T(n + 2, 2)A0089110 2 12 40 100 210 392 672 1080 1650 2420 3432 4732 6370 8400 10880 13872 17442 21660 26600 32340
Inv:RevDiagCol3T(n + 3, 3)missing0 -7 -70 -350 -1225 -3430 -8232 -17640 -34650 -63525 -110110 -182182 -289835 -445900 -666400
Inv:RevPolysee docsmissing1 1 1 1 1 1 1 0 1 1 1 0 -1 1 1 1 0 3 -2 1 1 1 0 -19 10 -3 1 1 1 0 205 -98 21 -4 1 1 1 0 -3341 1600
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^kA0000271 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:RevPolyRow3 k=0..3 T(3, k) n^kA0141051 0 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:RevPolyCol2 k=0..n T(n, k) 2^kmissing1 1 -1 3 -19 205 -3341 76391 -2330343 91416249 -4482922489 268693075915 -19325695148475
Inv:RevPolyCol3 k=0..n T(n, k) 3^kmissing1 1 -2 10 -98 1600 -39212 1345834 -61596110 3624729616 -266632381448 23971865555176
Inv:RevPolyDiag k=0..n T(n, k) n^kmissing1 1 -1 10 -279 16576 -1810025 329192046 -92820081375 38421129293632 -22369273006852449
 << 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.