CHAINS[0] 1
[1] 2, 1
[2] 4, 5, 2
[3] 8, 19, 18, 6
[4] 16, 65, 110, 84, 24
[5] 32, 211, 570, 750, 480, 120

      OEIS Similars: A038719

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA0387191 2 1 4 5 2 8 19 18 6 16 65 110 84 24 32 211 570 750 480 120 64 665 2702 5460 5880 3240 720 128
StdRevT(n, n - k), 0 ≤ k ≤ nmissing1 1 2 2 5 4 6 18 19 8 24 84 110 65 16 120 480 750 570 211 32 720 3240 5880 5460 2702 665 64 5040
StdAccsee docsmissing1 2 3 4 9 11 8 27 45 51 16 81 191 275 299 32 243 813 1563 2043 2163 64 729 3431 8891 14771 18011
StdAccRevsee docsmissing1 1 3 2 7 11 6 24 43 51 24 108 218 283 299 120 600 1350 1920 2131 2163 720 3960 9840 15300 18002
StdAntiDiagsee docsmissing1 2 4 1 8 5 16 19 2 32 65 18 64 211 110 6 128 665 570 84 256 2059 2702 750 24 512 6305 12138 5460
StdDiffx1T(n, k) (k+1)A1994001 2 2 4 10 6 8 38 54 24 16 130 330 336 120 32 422 1710 3000 2400 720 64 1330 8106 21840 29400 19440
StdRowSum k=0..n T(n, k)A0070471 3 11 51 299 2163 18731 189171 2183339 28349043 408990251 6490530291 112366270379 2107433393523
StdEvenSum k=0..n T(n, k) even(k)A0006291 2 6 26 150 1082 9366 94586 1091670 14174522 204495126 3245265146 56183135190 1053716696762
StdOddSum k=0..n T(n, k) odd(k)A0020500 1 5 25 149 1081 9365 94585 1091669 14174521 204495125 3245265145 56183135189 1053716696761
StdAltSum 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
StdAbsSum k=0..n | T(n, k) |A0070471 3 11 51 299 2163 18731 189171 2183339 28349043 408990251 6490530291 112366270379 2107433393523
StdDiagSum k=0..n // 2 T(n - k, k)missing1 2 5 13 37 115 391 1447 5791 24895 114271 557167 2873071 15608815 89047471 531915247 3318324271
StdAccSum k=0..n j=0..k T(n, j)missing1 5 24 131 862 6857 64628 705455 8750538 121518869 1867112992 31439023739 575594223734
StdAccRevSum k=0..n j=0..k T(n, n - j)A1625091 4 20 124 932 8284 85220 997084 13082852 190320604 3040770020 52937870044 997533561572
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 20 1368 240240 48108000 60545983680 1044991435017600 956036236766889358080
StdRowGcdGcd k=0..n | T(n, k) | > 1A0000121 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 2 5 19 110 750 5880 57120 650160 8013600 106444800 1699624080 28765376640 512898946560
StdColMiddleT(n, n // 2)missing1 2 5 19 110 570 5460 35406 484344 3759840 67609080 610563360 13689149760 140915174400
StdCentralET(2 n, n)missing1 5 110 5460 484344 67609080 13689149760 3798425030400 1385146411608960 642816232339881600
StdCentralOT(2 n + 1, n)missing2 19 570 35406 3759840 610563360 140915174400 43888511787120 17748253957674240 9045150240092803200
StdColLeftT(n, 0)A0000791 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
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)A0002721 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 56693912375296
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -1 -4 1 104 543 -3116 -78283 -372688 8914267 191686604 374581161 -54397789304 -1053278209609
StdTransNat0 k=0..n T(n, k) kmissing0 1 9 73 633 6121 66489 807913 10899513 161971561 2631779769 46447339753 885167291193
StdTransNat1 k=0..n T(n, k) (k + 1)A1625091 4 20 124 932 8284 85220 997084 13082852 190320604 3040770020 52937870044 997533561572
StdTransSqrs k=0..n T(n, k) k^2missing0 1 13 145 1645 19921 261613 3739345 58095085 977772241 17755615213 346443700945 7234250207725
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kmissing1 5 28 182 1408 13040 143008 1823792 26564608 435249920 7923647488 158673162752 3466332971008
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA1198811 -3 8 -18 32 -48 128 -528 512 6912 2048 -357888 8192 22351872 32768 -1903822848 131072
StdDiagRow1T(n + 1, n)A0387202 5 18 84 480 3240 25200 221760 2177280 23587200 279417600 3592512000 49816166400 741015475200
StdDiagRow2T(n + 2, n)missing4 19 110 750 5880 52080 514080 5594400 66528000 858211200 11935123200 177989011200 2833294464000
StdDiagRow3T(n + 3, n)missing8 65 570 5460 57120 650160 8013600 106444800 1516838400 23091868800 374140166400 6429398976000
StdDiagCol1T(n + 1, 1)A0010471 5 19 65 211 665 2059 6305 19171 58025 175099 527345 1586131 4766585 14316139 42981185 129009091
StdDiagCol2T(n + 2, 2)A0387212 18 110 570 2702 12138 52670 223290 931502 3842058 15718430 63928410 258885902 1045076778
StdDiagCol3T(n + 3, 3)missing6 84 750 5460 35406 213444 1225230 6796020 36774606 195399204 1024151310 5312541780 27339366606
StdPolysee docsmissing1 2 1 4 3 1 8 11 4 1 16 51 22 5 1 32 299 166 37 6 1 64 2163 1642 389 56 7 1 128 18731 20254 5413
StdPolyRow1 k=0..1 T(1, 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
StdPolyRow2 k=0..2 T(2, k) n^kA0848494 11 22 37 56 79 106 137 172 211 254 301 352 407 466 529 596 667 742 821 904 991 1082 1177 1276
StdPolyRow3 k=0..3 T(3, k) n^kmissing8 51 166 389 756 1303 2066 3081 4384 6011 7998 10381 13196 16479 20266 24593 29496 35011 41174
StdPolyCol2 k=0..n T(n, k) 2^kA3683191 4 22 166 1642 20254 299722 5174446 102094042 2266154014 55890234922 1516265078926 44874837768442
StdPolyCol3 k=0..n T(n, k) 3^kA3683221 5 37 389 5413 94085 1962277 47746949 1327769893 41538664325 1443908686117 55210237509509
StdPolyDiag k=0..n T(n, k) n^kmissing1 3 22 389 13556 784087 67687726 8140618761 1299685784968 265765828110011 67705436237351474
AltTriangleT(n, k), 0 ≤ k ≤ nA0387191 2 -1 4 -5 2 8 -19 18 -6 16 -65 110 -84 24 32 -211 570 -750 480 -120 64 -665 2702 -5460 5880 -3240
AltRevT(n, n - k), 0 ≤ k ≤ nmissing1 -1 2 2 -5 4 -6 18 -19 8 24 -84 110 -65 16 -120 480 -750 570 -211 32 720 -3240 5880 -5460 2702
AltAccsee docsmissing1 2 1 4 -1 1 8 -11 7 1 16 -49 61 -23 1 32 -179 391 -359 121 1 64 -601 2101 -3359 2521 -719 1 128
AltAccRevsee docsA1308501 -1 1 2 -3 1 -6 12 -7 1 24 -60 50 -15 1 -120 360 -390 180 -31 1 720 -2520 3360 -2100 602 -63 1
AltAntiDiagsee docsmissing1 2 4 -1 8 -5 16 -19 2 32 -65 18 64 -211 110 -6 128 -665 570 -84 256 -2059 2702 -750 24 512 -6305
AltDiffx1T(n, k) (k+1)A1994001 2 -2 4 -10 6 8 -38 54 -24 16 -130 330 -336 120 32 -422 1710 -3000 2400 -720 64 -1330 8106 -21840
AltRowSum k=0..n T(n, k)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
AltEvenSum k=0..n T(n, k) even(k)A0006291 2 6 26 150 1082 9366 94586 1091670 14174522 204495126 3245265146 56183135190 1053716696762
AltOddSum k=0..n T(n, k) odd(k)A0020500 -1 -5 -25 -149 -1081 -9365 -94585 -1091669 -14174521 -204495125 -3245265145 -56183135189
AltAltSum k=0..n T(n, k) (-1)^kA0070471 3 11 51 299 2163 18731 189171 2183339 28349043 408990251 6490530291 112366270379 2107433393523
AltAbsSum k=0..n | T(n, k) |A0070471 3 11 51 299 2163 18731 189171 2183339 28349043 408990251 6490530291 112366270379 2107433393523
AltDiagSum k=0..n // 2 T(n - k, k)missing1 2 3 3 -1 -15 -43 -51 173 1365 4877 7749 -31747 -338235 -1629763 -4078011 9073853 179141445
AltAccSum k=0..n j=0..k T(n, j)A0000271 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
AltAccRevSum k=0..n j=0..k T(n, n - j)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
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 20 1368 240240 48108000 60545983680 1044991435017600 956036236766889358080
AltRowGcdGcd k=0..n | T(n, k) | > 1A0000121 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 2 5 19 110 750 5880 57120 650160 8013600 106444800 1699624080 28765376640 512898946560
AltColMiddleT(n, n // 2)missing1 2 -5 -19 110 570 -5460 -35406 484344 3759840 -67609080 -610563360 13689149760 140915174400
AltCentralET(2 n, n)missing1 -5 110 -5460 484344 -67609080 13689149760 -3798425030400 1385146411608960 -642816232339881600
AltCentralOT(2 n + 1, n)missing2 -19 570 -35406 3759840 -610563360 140915174400 -43888511787120 17748253957674240
AltColLeftT(n, 0)A0000791 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
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)missing1 1 -4 -1 104 -543 -3116 78283 -372688 -8914267 191686604 -374581161 -54397789304 1053278209609
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kA0002721 -3 16 -125 1296 -16807 262144 -4782969 100000000 -2357947691 61917364224 -1792160394037
AltTransNat0 k=0..n T(n, k) kA0000120 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
AltTransNat1 k=0..n T(n, k) (k + 1)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
AltTransSqrs k=0..n T(n, k) k^2A0106840 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kA1198811 3 8 18 32 48 128 528 512 -6912 2048 357888 8192 -22351872 32768 1903822848 131072 -209865080832
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 -5 28 -182 1408 -13040 143008 -1823792 26564608 -435249920 7923647488 -158673162752 3466332971008
AltDiagRow1T(n + 1, n)A0387202 -5 18 -84 480 -3240 25200 -221760 2177280 -23587200 279417600 -3592512000 49816166400
AltDiagRow2T(n + 2, n)missing4 -19 110 -750 5880 -52080 514080 -5594400 66528000 -858211200 11935123200 -177989011200
AltDiagRow3T(n + 3, n)missing8 -65 570 -5460 57120 -650160 8013600 -106444800 1516838400 -23091868800 374140166400
AltDiagCol1T(n + 1, 1)A001047-1 -5 -19 -65 -211 -665 -2059 -6305 -19171 -58025 -175099 -527345 -1586131 -4766585 -14316139
AltDiagCol2T(n + 2, 2)A0387212 18 110 570 2702 12138 52670 223290 931502 3842058 15718430 63928410 258885902 1045076778
AltDiagCol3T(n + 3, 3)missing-6 -84 -750 -5460 -35406 -213444 -1225230 -6796020 -36774606 -195399204 -1024151310 -5312541780
AltPolysee docsmissing1 2 1 4 1 1 8 1 0 1 16 1 2 -1 1 32 1 -6 7 -2 1 64 1 38 -49 16 -3 1 128 1 -270 487 -164 29 -4 1 256
AltPolyRow1 k=0..1 T(1, k) n^kA0000272 1 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
AltPolyRow2 k=0..2 T(2, k) n^kA1308834 1 2 7 16 29 46 67 92 121 154 191 232 277 326 379 436 497 562 631 704 781 862 947 1036 1129 1226
AltPolyRow3 k=0..3 T(3, k) n^kmissing8 1 -6 -49 -164 -387 -754 -1301 -2064 -3079 -4382 -6009 -7996 -10379 -13194 -16477 -20264 -24591
AltPolyCol2 k=0..n T(n, k) 2^kA0528411 0 2 -6 38 -270 2342 -23646 272918 -3543630 51123782 -811316286 14045783798 -263429174190
AltPolyCol3 k=0..n T(n, k) 3^kmissing1 -1 7 -49 487 -6001 88807 -1533169 30250087 -671453041 16560069607 -449263727089 13296248227687
AltPolyDiag k=0..n T(n, k) n^kmissing1 1 2 -49 2284 -155523 14932546 -1935629141 326729376632 -69749414722567 18388604828150974
RevTriangleT(n, k), 0 ≤ k ≤ nmissing1 1 2 2 5 4 6 18 19 8 24 84 110 65 16 120 480 750 570 211 32 720 3240 5880 5460 2702 665 64 5040
RevAccsee docsmissing1 1 3 2 7 11 6 24 43 51 24 108 218 283 299 120 600 1350 1920 2131 2163 720 3960 9840 15300 18002
RevAccRevsee docsmissing1 2 3 4 9 11 8 27 45 51 16 81 191 275 299 32 243 813 1563 2043 2163 64 729 3431 8891 14771 18011
RevAntiDiagsee docsmissing1 1 2 2 6 5 24 18 4 120 84 19 720 480 110 8 5040 3240 750 65 40320 25200 5880 570 16 362880 221760
RevDiffx1T(n, k) (k+1)missing1 1 4 2 10 12 6 36 57 32 24 168 330 260 80 120 960 2250 2280 1055 192 720 6480 17640 21840 13510
RevRowSum k=0..n T(n, k)A0070471 3 11 51 299 2163 18731 189171 2183339 28349043 408990251 6490530291 112366270379 2107433393523
RevEvenSum k=0..n T(n, k) even(k)missing1 1 6 25 150 1081 9366 94585 1091670 14174521 204495126 3245265145 56183135190 1053716696761
RevOddSum k=0..n T(n, k) odd(k)missing0 2 5 26 149 1082 9365 94586 1091669 14174522 204495125 3245265146 56183135189 1053716696762
RevAbsSum k=0..n | T(n, k) |A0070471 3 11 51 299 2163 18731 189171 2183339 28349043 408990251 6490530291 112366270379 2107433393523
RevDiagSum k=0..n // 2 T(n - k, k)missing1 1 4 11 46 223 1318 9095 71986 642391 6380014 69784631 833457346 10791377143 150556177678
RevAccSum k=0..n j=0..k T(n, j)A1625091 4 20 124 932 8284 85220 997084 13082852 190320604 3040770020 52937870044 997533561572
RevAccRevSum k=0..n j=0..k T(n, n - j)missing1 5 24 131 862 6857 64628 705455 8750538 121518869 1867112992 31439023739 575594223734
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 20 1368 240240 48108000 60545983680 1044991435017600 956036236766889358080
RevRowGcdGcd k=0..n | T(n, k) | > 1A0000121 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 2 5 19 110 750 5880 57120 650160 8013600 106444800 1699624080 28765376640 512898946560
RevColMiddleT(n, n // 2)missing1 1 5 18 110 750 5460 57120 484344 6972840 67609080 1253221200 13689149760 312446534400
RevCentralET(2 n, n)missing1 5 110 5460 484344 67609080 13689149760 3798425030400 1385146411608960 642816232339881600
RevCentralOT(2 n + 1, n)missing1 18 750 57120 6972840 1253221200 312446534400 103403831731200 43916540610983040
RevColLeftT(n, 0)A0001421 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200
RevColRightT(n, n)A0000791 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
RevBinConv k=0..n C(n, k) T(n, k)A0002721 3 16 125 1296 16807 262144 4782969 100000000 2357947691 61917364224 1792160394037 56693912375296
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 1 -4 -1 104 -543 -3116 78283 -372688 -8914267 191686604 -374581161 -54397789304 1053278209609
RevTransNat0 k=0..n T(n, k) kmissing0 2 13 80 563 4694 45897 516284 6567199 93169826 1458122741 24948493448 463227953355 9275098265198
RevTransNat1 k=0..n T(n, k) (k + 1)missing1 5 24 131 862 6857 64628 705455 8750538 121518869 1867112992 31439023739 575594223734
RevTransSqrs k=0..n T(n, k) k^2missing0 2 21 166 1365 12786 138061 1697942 23436573 358556626 6019044933 109956391590 2170978153669
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA3683191 4 22 166 1642 20254 299722 5174446 102094042 2266154014 55890234922 1516265078926 44874837768442
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0528411 0 2 -6 38 -270 2342 -23646 272918 -3543630 51123782 -811316286 14045783798 -263429174190
RevDiagRow1T(n + 1, n)A0010471 5 19 65 211 665 2059 6305 19171 58025 175099 527345 1586131 4766585 14316139 42981185 129009091
RevDiagRow2T(n + 2, n)A0387212 18 110 570 2702 12138 52670 223290 931502 3842058 15718430 63928410 258885902 1045076778
RevDiagRow3T(n + 3, n)missing6 84 750 5460 35406 213444 1225230 6796020 36774606 195399204 1024151310 5312541780 27339366606
RevDiagCol1T(n + 1, 1)A0387202 5 18 84 480 3240 25200 221760 2177280 23587200 279417600 3592512000 49816166400 741015475200
RevDiagCol2T(n + 2, 2)missing4 19 110 750 5880 52080 514080 5594400 66528000 858211200 11935123200 177989011200 2833294464000
RevDiagCol3T(n + 3, 3)missing8 65 570 5460 57120 650160 8013600 106444800 1516838400 23091868800 374140166400 6429398976000
RevPolysee docsmissing1 1 1 2 3 1 6 11 5 1 24 51 28 7 1 120 299 182 53 9 1 720 2163 1408 447 86 11 1 5040 18731 13040
RevPolyRow1 k=0..1 T(1, 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
RevPolyRow2 k=0..2 T(2, k) n^kA0545522 11 28 53 86 127 176 233 298 371 452 541 638 743 856 977 1106 1243 1388 1541 1702 1871 2048 2233
RevPolyRow3 k=0..3 T(3, k) n^kmissing6 51 182 447 894 1571 2526 3807 5462 7539 10086 13151 16782 21027 25934 31551 37926 45107 53142
RevPolyCol2 k=0..n T(n, k) 2^kmissing1 5 28 182 1408 13040 143008 1823792 26564608 435249920 7923647488 158673162752 3466332971008
RevPolyCol3 k=0..n T(n, k) 3^kmissing1 7 53 447 4317 48567 637893 9689967 167850477 3269439207 70753134933 1684244512287 43737334717437
RevPolyDiag k=0..n T(n, k) n^kmissing1 3 28 447 10376 324395 13070016 658991487 40670238592 3016813197699 264769063500800
 << 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.