CATALANINV[0] 1
[1] 0, 1
[2] 0, 2, 1
[3] 0, 3, 4, 1
[4] 0, 4, 10, 6, 1
[5] 0, 5, 20, 21, 8, 1

      OEIS Similars: A128908, A053122, A078812, A285072

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(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 8 84 252
StdRevT(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 14 78 220
StdInvT-1(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
StdRevInvT-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
StdAccsee docsmissing1 0 1 0 2 3 0 3 7 8 0 4 14 20 21 0 5 25 46 54 55 0 6 41 97 133 143 144 0 7 63 189 309 364 376 377 0
StdAccRevsee docsmissing1 1 1 1 3 3 1 5 8 8 1 7 17 21 21 1 9 30 50 55 55 1 11 47 103 138 144 144 1 13 68 188 314 370 377
StdAntiDiagsee 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 10 120 252 120
StdDiffx1T(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 14 168 504 600 330 84 8 0
StdRowSum 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
StdEvenSum 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 19544084
StdOddSum 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 19544085
StdAltSum k=0..n T(n, k) (-1)^kA0116551 -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
StdAbsSum 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
StdDiagSum 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 524288 1048576
StdAccSum k=0..n j=0..k T(n, j)A3778661 1 5 18 59 185 564 1685 4957 14406 41455 118321 335400 945193 2650229 7398330 20573219 57013865
StdAccRevSum k=0..n j=0..k T(n, n - j)A2909171 2 7 22 67 200 588 1708 4913 14018 39725 111922 313752 875702 2434747 6746350 18636343 51340988
StdRowLcmLcm k=0..n | T(n, k) | > 1A0999961 1 2 12 60 840 2520 27720 360360 720720 12252240 232792560 232792560 5354228880 26771144400
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 4 10 21 56 126 330 792 2002 5005 12376 31824 77520 203490 497420 1307504 3268760 8436285
StdColMiddleT(n, n // 2)missing1 0 2 3 10 20 56 126 330 792 2002 5005 12376 31824 77520 203490 490314 1307504 3124550 8436285
StdCentralET(2 n, n)A1658171 2 10 56 330 2002 12376 77520 490314 3124550 20030010 129024480 834451800 5414950296 35240152720
StdCentralOT(2 n + 1, n)missing0 3 20 126 792 5005 31824 203490 1307504 8436285 54627300 354817320 2310789600 15084504396
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)A2624401 1 5 22 101 476 2282 11075 54245 267592 1327580 6617128 33110090 166215895 836761343 4222640822
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA3502901 1 -3 -2 21 -4 -150 155 1029 -2072 -6468 22056 34122 -208857 -106249 1816958 -639067 -14629264
StdTransNat0 k=0..n T(n, k) kA0302670 1 4 14 46 145 444 1331 3926 11434 32960 94211 267384 754309 2116936 5914310 16458034 45638101
StdTransNat1 k=0..n T(n, k) (k + 1)A2909171 2 7 22 67 200 588 1708 4913 14018 39725 111922 313752 875702 2434747 6746350 18636343 51340988
StdTransSqrs k=0..n T(n, k) k^2missing0 1 6 28 114 427 1512 5141 16950 54548 172146 534575 1637712 4959697 14871390 44206156 130407738
StdPosHalf 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
StdNegHalf 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
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)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
StdDiagRow3T(n + 3, n)A0024920 4 20 56 120 220 364 560 816 1140 1540 2024 2600 3276 4060 4960 5984 7140 8436 9880 11480 13244
StdDiagCol1T(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 32 33 34 35 36
StdDiagCol2T(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 2600 2925
StdDiagCol3T(n + 3, 3)A0003891 6 21 56 126 252 462 792 1287 2002 3003 4368 6188 8568 11628 15504 20349 26334 33649 42504 53130
StdPolysee docsmissing1 0 1 0 1 1 0 3 2 1 0 8 8 3 1 0 21 30 15 4 1 0 55 112 72 24 5 1 0 144 418 345 140 35 6 1 0 377 1560
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^kA3176370 8 30 72 140 240 378 560 792 1080 1430 1848 2340 2912 3570 4320 5168 6120 7182 8360 9660 11088
StdPolyCol2 k=0..n T(n, k) 2^kA0525301 2 8 30 112 418 1560 5822 21728 81090 302632 1129438 4215120 15731042 58709048 219105150 817711552
StdPolyCol3 k=0..n T(n, k) 3^kA2909021 3 15 72 345 1653 7920 37947 181815 871128 4173825 19997997 95816160 459082803 2199597855
StdPolyDiag k=0..n T(n, k) n^kmissing1 1 8 72 816 11275 184464 3493847 75279680 1819587240 48783168600 1437161758021 46160634789360
AltInvT-1(n, k), 0 ≤ k ≤ nmissing1 0 1 0 2 1 0 -5 -4 1 0 -46 -34 6 1 0 228 168 -27 -8 1 0 3592 2645 -430 -116 10 1 0 -25779 -18980
AltRevInvT-1(n, n - k), 0 ≤ k ≤ nmissing1 1 0 1 2 0 1 -4 -5 0 1 6 -34 -46 0 1 -8 -27 168 228 0 1 10 -116 -430 2645 3592 0 1 -12 -65 832
AltAccsee 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
AltAccRevsee 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
AltDiffx1T(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
AltRowSum k=0..n T(n, k)A0116551 -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
AltEvenSum 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 19544084
AltOddSum 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
AltAltSum 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
AltAbsSum 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
AltDiagSum k=0..n // 2 T(n - k, k)A0095451 0 -1 -2 -2 0 4 8 8 0 -16 -32 -32 0 64 128 128 0 -256 -512 -512 0 1024 2048 2048 0 -4096 -8192
AltAccSum 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
AltAccRevSum 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
AltRowLcmLcm k=0..n | T(n, k) | > 1A0999961 1 2 12 60 840 2520 27720 360360 720720 12252240 232792560 232792560 5354228880 26771144400
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 4 10 21 56 126 330 792 2002 5005 12376 31824 77520 203490 497420 1307504 3268760 8436285
AltColMiddleT(n, n // 2)missing1 0 -2 -3 10 20 -56 -126 330 792 -2002 -5005 12376 31824 -77520 -203490 490314 1307504 -3124550
AltCentralET(2 n, n)A1658171 -2 10 -56 330 -2002 12376 -77520 490314 -3124550 20030010 -129024480 834451800 -5414950296
AltCentralOT(2 n + 1, n)missing0 -3 20 -126 792 -5005 31824 -203490 1307504 -8436285 54627300 -354817320 2310789600 -15084504396
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)A3502901 -1 -3 2 21 4 -150 -155 1029 2072 -6468 -22056 34122 208857 -106249 -1816958 -639067 14629264
AltInvBinConv 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
AltTransNat0 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
AltTransNat1 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
AltTransSqrs 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 36
AltPosHalf 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
AltNegHalf 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
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)A0141050 -3 10 -21 36 -55 78 -105 136 -171 210 -253 300 -351 406 -465 528 -595 666 -741 820 -903 990 -1081
AltDiagRow3T(n + 3, n)A0024920 -4 20 -56 120 -220 364 -560 816 -1140 1540 -2024 2600 -3276 4060 -4960 5984 -7140 8436 -9880
AltDiagCol1T(n + 1, 1)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
AltDiagCol2T(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 2600 2925
AltDiagCol3T(n + 3, 3)A000389-1 -6 -21 -56 -126 -252 -462 -792 -1287 -2002 -3003 -4368 -6188 -8568 -11628 -15504 -20349 -26334
AltPolysee 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
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 0 2 0 -12 -40 -90 -168 -280 -432 -630 -880 -1188 -1560 -2002 -2520 -3120 -3808 -4590 -5472 -6460
AltPolyCol2 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
AltPolyCol3 k=0..n T(n, k) 3^kA0841031 -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
AltPolyDiag k=0..n T(n, k) n^kmissing1 -1 0 0 16 -275 4680 -88543 1883328 -44791056 1181184400 -34254174229 1084253219280
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 14 78 220
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
RevAccsee docsmissing1 1 1 1 3 3 1 5 8 8 1 7 17 21 21 1 9 30 50 55 55 1 11 47 103 138 144 144 1 13 68 188 314 370 377
RevAccRevsee docsmissing1 0 1 0 2 3 0 3 7 8 0 4 14 20 21 0 5 25 46 54 55 0 6 41 97 133 143 144 0 7 63 189 309 364 376 377 0
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 18 105 220
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 24 165 480 630 336 49 0 1
RevRowSum 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
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
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 7465176 19544084
RevAltSum k=0..n T(n, k) (-1)^kA3296821 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
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
RevDiagSum k=0..n // 2 T(n - k, k)A1589431 1 1 3 5 10 19 36 69 131 250 476 907 1728 3292 6272 11949 22765 43371 82629 157422 299915 571388
RevAccSum k=0..n j=0..k T(n, j)A2909171 2 7 22 67 200 588 1708 4913 14018 39725 111922 313752 875702 2434747 6746350 18636343 51340988
RevAccRevSum k=0..n j=0..k T(n, n - j)A3778661 1 5 18 59 185 564 1685 4957 14406 41455 118321 335400 945193 2650229 7398330 20573219 57013865
RevRowLcmLcm k=0..n | T(n, k) | > 1A0999961 1 2 12 60 840 2520 27720 360360 720720 12252240 232792560 232792560 5354228880 26771144400
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 4 10 21 56 126 330 792 2002 5005 12376 31824 77520 203490 497420 1307504 3268760 8436285
RevColMiddleT(n, n // 2)missing1 1 2 4 10 21 56 120 330 715 2002 4368 12376 27132 77520 170544 490314 1081575 3124550 6906900
RevCentralET(2 n, n)A1658171 2 10 56 330 2002 12376 77520 490314 3124550 20030010 129024480 834451800 5414950296 35240152720
RevCentralOT(2 n + 1, n)A0457211 4 21 120 715 4368 27132 170544 1081575 6906900 44352165 286097760 1852482996 12033222880
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)A2624401 1 5 22 101 476 2282 11075 54245 267592 1327580 6617128 33110090 166215895 836761343 4222640822
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA3502901 -1 -3 2 21 4 -150 -155 1029 2072 -6468 -22056 34122 208857 -106249 -1816958 -639067 14629264
RevTransNat0 k=0..n T(n, k) kA2811990 0 2 10 38 130 420 1308 3970 11822 34690 100610 289032 823800 2332418 6566290 18394910 51310978
RevTransNat1 k=0..n T(n, k) (k + 1)A3778661 1 5 18 59 185 564 1685 4957 14406 41455 118321 335400 945193 2650229 7398330 20573219 57013865
RevTransSqrs k=0..n T(n, k) k^2missing0 0 2 16 82 352 1368 4980 17302 58040 189446 604964 1897488 5863080 17888138 53985856 161397754
RevPosHalf 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 817711552
RevNegHalf 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
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 32 33 34 35 36
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 2600 2925
RevDiagRow3T(n + 3, n)A0003891 6 21 56 126 252 462 792 1287 2002 3003 4368 6188 8568 11628 15504 20349 26334 33649 42504 53130
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)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
RevDiagCol3T(n + 3, 3)A0024920 4 20 56 120 220 364 560 816 1140 1540 2024 2600 3276 4060 4960 5984 7140 8436 9880 11480 13244
RevPolysee docsmissing1 1 1 1 1 1 1 3 1 1 1 8 5 1 1 1 21 21 7 1 1 1 55 85 40 9 1 1 1 144 341 217 65 11 1 1 1 377 1365
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^kA0005671 8 21 40 65 96 133 176 225 280 341 408 481 560 645 736 833 936 1045 1160 1281 1408 1541 1680 1825
RevPolyCol2 k=0..n T(n, k) 2^kA0024501 1 5 21 85 341 1365 5461 21845 87381 349525 1398101 5592405 22369621 89478485 357913941 1431655765
RevPolyCol3 k=0..n T(n, k) 3^kA0994591 1 7 40 217 1159 6160 32689 173383 919480 4875913 25856071 137109280 727060321 3855438727
RevPolyDiag k=0..n T(n, k) n^kmissing1 1 5 40 441 6191 105469 2111201 48524273 1258634440 36350423781 1156426099511 40170363882025
InvTriangleT(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
InvRevT(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
InvRevInvT-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 14 78 220
InvAccsee 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 -143 286 78
InvAccRevsee 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 -154 275 -297
InvAntiDiagsee 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
InvDiffx1T(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
InvRowSum k=0..n T(n, k)A0001081 1 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670
InvEvenSum 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
InvOddSum 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
InvAltSum k=0..n T(n, k) (-1)^kA0017001 -1 3 -10 35 -126 462 -1716 6435 -24310 92378 -352716 1352078 -5200300 20058300 -77558760
InvAbsSum k=0..n | T(n, k) |A0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
InvDiagSum 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
InvAccSum 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 -164812365
InvAccRevSum 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 35357670
InvRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 20 42 3024 660 34320 450450 13613600 4232592 1777688640 240253860 144152316000 516300642000
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 5 14 48 165 572 2002 7072 25194 90440 326876 1225785 4601610 17298645 65132550 245642760
InvColMiddleT(n, n // 2)missing1 0 -2 5 14 -48 -110 429 910 -3808 -7752 33915 67298 -303600 -592020 2731365 5259150 -24682944
InvCentralET(2 n, n)A3591081 -2 14 -110 910 -7752 67298 -592020 5259150 -47071640 423830264 -3834669566 34834267234
InvCentralOT(2 n + 1, n)missing0 5 -48 429 -3808 33915 -303600 2731365 -24682944 223926516 -2038362560 18609425835 -170333048928
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 -3 4 5 -39 84 8 -603 1795 -1243 -9096 37388 -50036 -119640 747984 -1460827 -1006569 14187927
InvInvBinConv 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 17620076360
InvTransNat0 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
InvTransNat1 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 35357670
InvTransSqrs 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
InvPosHalf 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
InvNegHalf 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
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)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
InvDiagRow3T(n + 3, n)missing0 -14 -48 -110 -208 -350 -544 -798 -1120 -1518 -2000 -2574 -3248 -4030 -4928 -5950 -7104 -8398
InvDiagCol1T(n + 1, 1)A0001081 -2 5 -14 42 -132 429 -1430 4862 -16796 58786 -208012 742900 -2674440 9694845 -35357670 129644790
InvDiagCol2T(n + 2, 2)A0020571 -4 14 -48 165 -572 2002 -7072 25194 -90440 326876 -1188640 4345965 -15967980 58929450 -218349120
InvDiagCol3T(n + 3, 3)A0035171 -6 27 -110 429 -1638 6188 -23256 87210 -326876 1225785 -4601610 17298645 -65132550 245642760
InvPolysee 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 -36 18 40 50
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 2 2 6 20 50 102 182 296 450 650 902 1212 1586 2030 2550 3152 3842 4626 5510 6500 7602 8822 10166
InvPolyCol2 k=0..n T(n, k) 2^kmissing1 2 0 2 -4 12 -36 114 -372 1244 -4240 14676 -51448 182288 -651756 2348562 -8520564 31097388
InvPolyCol3 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
InvPolyDiag k=0..n T(n, k) n^kmissing1 1 0 6 40 510 7308 126924 2546640 58123350 1485935440 42059272596 1305569973552 44095635642604
Inv: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
Inv:RevRevT(n, 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
Inv: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 8 84 252
Inv:RevAccsee 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 -154 275 -297
Inv:RevAccRevsee 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 -143 286 78
Inv: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
Inv: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
Inv:RevRowSum k=0..n T(n, k)A0001081 1 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670
Inv: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
Inv: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
Inv:RevAltSum k=0..n T(n, k) (-1)^kA0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
Inv:RevAbsSum k=0..n | T(n, k) |A0017001 1 3 10 35 126 462 1716 6435 24310 92378 352716 1352078 5200300 20058300 77558760 300540195
Inv:RevDiagSum k=0..n // 2 T(n - k, k)missing1 1 1 -1 -3 0 7 4 -15 -16 32 49 -73 -139 188 393 -551 -1149 1776 3523 -6040 -11310 21089 37669
Inv:RevAccSum k=0..n j=0..k T(n, j)A0001081 2 -1 2 -5 14 -42 132 -429 1430 -4862 16796 -58786 208012 -742900 2674440 -9694845 35357670
Inv:RevAccRevSum k=0..n j=0..k T(n, n - j)A0386651 1 -3 8 -25 84 -294 1056 -3861 14300 -53482 201552 -764218 2912168 -11143500 42791040 -164812365
Inv:RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 1 2 20 42 3024 660 34320 450450 13613600 4232592 1777688640 240253860 144152316000 516300642000
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 5 14 48 165 572 2002 7072 25194 90440 326876 1225785 4601610 17298645 65132550 245642760
Inv:RevColMiddleT(n, n // 2)missing1 1 -2 -4 14 27 -110 -208 910 1700 -7752 -14364 67298 123970 -592020 -1085760 5259150 9612108
Inv:RevCentralET(2 n, n)A3591081 -2 14 -110 910 -7752 67298 -592020 5259150 -47071640 423830264 -3834669566 34834267234
Inv:RevCentralOT(2 n + 1, n)A0260051 -4 27 -208 1700 -14364 123970 -1085760 9612108 -85795600 770755843 -6960408624 63127818572
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 -3 4 5 -39 84 8 -603 1795 -1243 -9096 37388 -50036 -119640 747984 -1460827 -1006569 14187927
Inv:RevInvBinConv 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
Inv:RevTransNat0 k=0..n T(n, k) kA0009840 0 -2 6 -20 70 -252 924 -3432 12870 -48620 184756 -705432 2704156 -10400600 40116600 -155117520
Inv:RevTransNat1 k=0..n T(n, k) (k + 1)A0386651 1 -3 8 -25 84 -294 1056 -3861 14300 -53482 201552 -764218 2912168 -11143500 42791040 -164812365
Inv:RevTransSqrs k=0..n T(n, k) k^2missing0 0 -2 16 -76 340 -1484 6384 -27192 114972 -483340 2022592 -8431592 35036456 -145192376 600263200
Inv:RevPosHalf 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 31097388
Inv:RevNegHalf 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
Inv:RevDiagRow1T(n + 1, n)A0001081 -2 5 -14 42 -132 429 -1430 4862 -16796 58786 -208012 742900 -2674440 9694845 -35357670 129644790
Inv:RevDiagRow2T(n + 2, n)A0020571 -4 14 -48 165 -572 2002 -7072 25194 -90440 326876 -1188640 4345965 -15967980 58929450 -218349120
Inv:RevDiagRow3T(n + 3, n)A0035171 -6 27 -110 429 -1638 6188 -23256 87210 -326876 1225785 -4601610 17298645 -65132550 245642760
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)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
Inv:RevDiagCol3T(n + 3, 3)missing0 -14 -48 -110 -208 -350 -544 -798 -1120 -1518 -2000 -2574 -3248 -4030 -4928 -5950 -7104 -8398
Inv:RevPolysee docsmissing1 1 1 1 1 1 1 -1 1 1 1 2 -3 1 1 1 -5 13 -5 1 1 1 14 -67 34 -7 1 1 1 -42 381 -269 65 -9 1 1 1 132
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^kA1908161 2 13 34 65 106 157 218 289 370 461 562 673 794 925 1066 1217 1378 1549 1730 1921 2122 2333 2554
Inv:RevPolyCol2 k=0..n T(n, k) 2^kA0640621 1 -3 13 -67 381 -2307 14589 -95235 636925 -4341763 30056445 -210731011 1493303293 -10678370307
Inv:RevPolyCol3 k=0..n T(n, k) 3^kA3713911 1 -5 34 -269 2326 -21314 203428 -2000957 20142862 -206524790 2149261852 -22644243218 241061343004
Inv:RevPolyDiag k=0..n T(n, k) n^kmissing1 1 -3 34 -695 20886 -834827 41819604 -2524235247 178542465670 -14494402912979 1329048210876156
 << 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.