SYLVESTER[0] 1
[1] 0, 2
[2] 0, 1, 4
[3] 0, 2, 6, 8
[4] 0, 6, 19, 24, 16
[5] 0, 24, 80, 110, 80, 32

      OEIS Similars: A341101

↕ Type↕ Trait↕ Anum↕ Sequence
StdTriangleT(n, k), 0 ≤ k ≤ nA3411011 0 2 0 1 4 0 2 6 8 0 6 19 24 16 0 24 80 110 80 32 0 120 418 615 500 240 64 0 720 2604 4046 3570
StdRevT(n, n - k), 0 ≤ k ≤ nmissing1 2 0 4 1 0 8 6 2 0 16 24 19 6 0 32 80 110 80 24 0 64 240 500 615 418 120 0 128 672 1960 3570 4046
StdAccsee docsmissing1 0 2 0 1 5 0 2 8 16 0 6 25 49 65 0 24 104 214 294 326 0 120 538 1153 1653 1893 1957 0 720 3324
StdAccRevsee docsmissing1 2 2 4 5 5 8 14 16 16 16 40 59 65 65 32 112 222 302 326 326 64 304 804 1419 1837 1957 1957 128 800
StdAntiDiagsee docsmissing1 0 0 2 0 1 0 2 4 0 6 6 0 24 19 8 0 120 80 24 0 720 418 110 16 0 5040 2604 615 80 0 40320 18828
StdDiffx1T(n, k) (k+1)missing1 0 4 0 2 12 0 4 18 32 0 12 57 96 80 0 48 240 440 400 192 0 240 1254 2460 2500 1440 448 0 1440 7812
StdRowSum k=0..n T(n, k)A0005221 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805
StdEvenSum k=0..n T(n, k) even(k)missing1 0 4 6 35 160 982 6846 54805 493200 4932056 54252550 651030679 8463398736 118487582410
StdOddSum k=0..n T(n, k) odd(k)missing0 2 1 10 30 166 975 6854 54796 493210 4932045 54252562 651030666 8463398750 118487582395
StdAltSum k=0..n T(n, k) (-1)^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
StdAbsSum k=0..n | T(n, k) |A0005221 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805
StdDiagSum k=0..n // 2 T(n - k, k)missing1 0 2 1 6 12 51 224 1264 8339 63726 552238 5351033 57309548 672108878 8564808105 117824815906
StdAccSum k=0..n j=0..k T(n, j)missing1 2 6 26 145 962 7314 62526 593737 6204370 70795718 876281826 11697961961 167578760338
StdAccRevSum k=0..n j=0..k T(n, n - j)missing1 4 14 54 245 1320 8342 60774 502273 4646140 47573494 534284630 6530896869 86323201952
StdRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 4 24 912 5280 205656000 2528588160 5874643821231360 916835503928037603840
StdRowGcdGcd k=0..n | T(n, k) | > 1A0000341 2 4 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
StdRowMaxMax k=0..n | T(n, k) |missing1 2 4 8 24 110 615 4046 30604 261656 2579380 28167920 334925404 4308766176 59645959464 884178662640
StdColMiddleT(n, n // 2)missing1 0 1 2 19 80 615 4046 28777 259056 1769985 20268050 135131755 1880186880 12330989671 202043487646
StdCentralET(2 n, n)missing1 1 19 615 28777 1769985 135131755 12330989671 1309509778577 158670146018241 21603959342147715
StdCentralOT(2 n + 1, n)missing0 2 80 4046 259056 20268050 1880186880 202043487646 24699845506336 3386443161237474
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)A0000791 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
StdBinConv k=0..n C(n, k) T(n, k)missing1 2 6 32 250 2452 28294 372276 5476902 88843388 1572182524 30095481528 618922505656 13596524483960
StdInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 2 2 -4 10 52 -626 3600 -4378 -209092 3583684 -37666352 228658456 1320343832 -74742710402
StdTransNat0 k=0..n T(n, k) kmissing0 2 9 38 180 994 6385 47074 392672 3659730 37709393 425779518 5228835524 69396404466 989898002665
StdTransNat1 k=0..n T(n, k) (k + 1)missing1 4 14 54 245 1320 8342 60774 502273 4646140 47573494 534284630 6530896869 86323201952
StdTransSqrs k=0..n T(n, k) k^2missing0 2 17 98 554 3414 23631 184134 1604396 15497994 164595605 1907674394 23971232006 324703850366
StdPosHalf k=0..n 2^n T(n, k) (1/2)^kA0842621 2 6 28 188 1656 17992 232016 3460368 58574368 1109200736 23230928832 533139875776 13304094478208
StdNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kmissing1 2 2 4 -4 56 -488 5552 -73456 1117216 -19197664 367902272 -7780394048 179998323584 -4522250011264
StdDiagRow1T(n + 1, n)A0017880 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008
StdDiagRow2T(n + 2, n)missing0 2 19 110 500 1960 6944 22848 71040 211200 605440 1683968 4566016 12113920 31539200 80773120
StdDiagRow3T(n + 3, n)missing0 6 80 615 3570 17360 74592 292320 1066560 3674880 12080640 38182144 116712960 346644480 1004093440
StdDiagCol1T(n + 1, 1)A0001422 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200
StdDiagCol2T(n + 2, 2)missing4 6 19 80 418 2604 18828 154944 1429776 14620320 164089440 2005361280 26508781440 376870959360
StdDiagCol3T(n + 3, 3)missing8 24 110 615 4046 30604 261656 2495340 26263512 302411736 3781675872 51039346176 739493351424
StdPolysee docsmissing1 0 1 0 2 1 0 5 4 1 0 16 18 6 1 0 65 92 39 8 1 0 326 536 276 68 10 1 0 1957 3552 2133 616 105 12 1
StdPolyRow1 k=0..1 T(1, k) n^kA0058430 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
StdPolyRow2 k=0..2 T(2, k) n^kA0077420 5 18 39 68 105 150 203 264 333 410 495 588 689 798 915 1040 1173 1314 1463 1620 1785 1958 2139
StdPolyRow3 k=0..3 T(3, k) n^kmissing0 16 92 276 616 1160 1956 3052 4496 6336 8620 11396 14712 18616 23156 28380 34336 41072 48636 57076
StdPolyCol2 k=0..n T(n, k) 2^kA0819231 4 18 92 536 3552 26608 223456 2085504 21450752 241320704 2949474816 38933066752 552141672448
StdPolyCol3 k=0..n T(n, k) 3^kmissing1 6 39 276 2133 18018 166203 1670112 18221193 215014014 2733237999 37281387564 543586734621
StdPolyDiag k=0..n T(n, k) n^kA2951831 2 18 276 5960 165870 5648832 227507336 10577029248 557457222330 32843470246400 2139014862736092
AltTriangleT(n, k), 0 ≤ k ≤ nA3411011 0 -2 0 -1 4 0 -2 6 -8 0 -6 19 -24 16 0 -24 80 -110 80 -32 0 -120 418 -615 500 -240 64 0 -720 2604
AltRevT(n, n - k), 0 ≤ k ≤ nmissing1 -2 0 4 -1 0 -8 6 -2 0 16 -24 19 -6 0 -32 80 -110 80 -24 0 64 -240 500 -615 418 -120 0 -128 672
AltAccsee docsmissing1 0 -2 0 -1 3 0 -2 4 -4 0 -6 13 -11 5 0 -24 56 -54 26 -6 0 -120 298 -317 183 -57 7 0 -720 1884
AltAccRevsee docsmissing1 -2 -2 4 3 3 -8 -2 -4 -4 16 -8 11 5 5 -32 48 -62 18 -6 -6 64 -176 324 -291 127 7 7 -128 544 -1416
AltAntiDiagsee docsmissing1 0 0 -2 0 -1 0 -2 4 0 -6 6 0 -24 19 -8 0 -120 80 -24 0 -720 418 -110 16 0 -5040 2604 -615 80 0
AltDiffx1T(n, k) (k+1)missing1 0 -4 0 -2 12 0 -4 18 -32 0 -12 57 -96 80 0 -48 240 -440 400 -192 0 -240 1254 -2460 2500 -1440 448
AltRowSum k=0..n T(n, k)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
AltEvenSum k=0..n T(n, k) even(k)missing1 0 4 6 35 160 982 6846 54805 493200 4932056 54252550 651030679 8463398736 118487582410
AltOddSum k=0..n T(n, k) odd(k)missing0 -2 -1 -10 -30 -166 -975 -6854 -54796 -493210 -4932045 -54252562 -651030666 -8463398750
AltAltSum k=0..n T(n, k) (-1)^kA0005221 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805
AltAbsSum k=0..n | T(n, k) |A0005221 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805
AltDiagSum k=0..n // 2 T(n - k, k)missing1 0 -2 -1 2 0 -13 -64 -396 -2971 -25070 -235210 -2433799 -27549452 -338757350 -4497600521
AltAccSum k=0..n j=0..k T(n, j)missing1 -2 2 -2 1 -2 -6 -30 -199 -1426 -11782 -108506 -1106167 -12363730 -150381214 -1977666774
AltAccRevSum k=0..n j=0..k T(n, n - j)missing1 -4 10 -18 29 -40 62 -42 289 1316 11914 108350 1106349 12363520 150381454 1977666502 27965386593
AltRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 4 24 912 5280 205656000 2528588160 5874643821231360 916835503928037603840
AltRowGcdGcd k=0..n | T(n, k) | > 1A0000341 2 4 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
AltRowMaxMax k=0..n | T(n, k) |missing1 2 4 8 24 110 615 4046 30604 261656 2579380 28167920 334925404 4308766176 59645959464 884178662640
AltColMiddleT(n, n // 2)missing1 0 -1 -2 19 80 -615 -4046 28777 259056 -1769985 -20268050 135131755 1880186880 -12330989671
AltCentralET(2 n, n)missing1 -1 19 -615 28777 -1769985 135131755 -12330989671 1309509778577 -158670146018241 21603959342147715
AltCentralOT(2 n + 1, n)missing0 -2 80 -4046 259056 -20268050 1880186880 -202043487646 24699845506336 -3386443161237474
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)A0000791 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048 4096 -8192 16384 -32768 65536 -131072 262144 -524288
AltBinConv k=0..n C(n, k) T(n, k)missing1 -2 2 4 10 -52 -626 -3600 -4378 209092 3583684 37666352 228658456 -1320343832 -74742710402
AltInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -2 6 -32 250 -2452 28294 -372276 5476902 -88843388 1572182524 -30095481528 618922505656
AltTransNat0 k=0..n T(n, k) kmissing0 -2 7 -14 24 -34 55 -34 280 1326 11903 108362 1106336 12363534 150381439 1977666518 27965386576
AltTransNat1 k=0..n T(n, k) (k + 1)missing1 -4 10 -18 29 -40 62 -42 289 1316 11914 108350 1106349 12363520 150381454 1977666502 27965386593
AltTransSqrs k=0..n T(n, k) k^2missing0 -2 15 -50 110 -214 321 -678 -172 -8202 -59125 -576234 -6007918 -68818814 -855799091 -11488399518
AltPosHalf k=0..n 2^n T(n, k) (1/2)^kmissing1 -2 2 -4 -4 -56 -488 -5552 -73456 -1117216 -19197664 -367902272 -7780394048 -179998323584
AltNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0842621 -2 6 -28 188 -1656 17992 -232016 3460368 -58574368 1109200736 -23230928832 533139875776
AltDiagRow1T(n + 1, n)A0017880 -1 6 -24 80 -240 672 -1792 4608 -11520 28160 -67584 159744 -372736 860160 -1966080 4456448
AltDiagRow2T(n + 2, n)missing0 -2 19 -110 500 -1960 6944 -22848 71040 -211200 605440 -1683968 4566016 -12113920 31539200
AltDiagRow3T(n + 3, n)missing0 -6 80 -615 3570 -17360 74592 -292320 1066560 -3674880 12080640 -38182144 116712960 -346644480
AltDiagCol1T(n + 1, 1)A000142-2 -1 -2 -6 -24 -120 -720 -5040 -40320 -362880 -3628800 -39916800 -479001600 -6227020800
AltDiagCol2T(n + 2, 2)missing4 6 19 80 418 2604 18828 154944 1429776 14620320 164089440 2005361280 26508781440 376870959360
AltDiagCol3T(n + 3, 3)missing-8 -24 -110 -615 -4046 -30604 -261656 -2495340 -26263512 -302411736 -3781675872 -51039346176
AltPolysee docsmissing1 0 1 0 -2 1 0 3 -4 1 0 -4 14 -6 1 0 5 -44 33 -8 1 0 -6 128 -168 60 -10 1 0 7 -352 801 -424 95 -12
AltPolyRow1 k=0..1 T(1, k) n^kA0058430 -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
AltPolyRow2 k=0..2 T(2, k) n^kA0339910 3 14 33 60 95 138 189 248 315 390 473 564 663 770 885 1008 1139 1278 1425 1580 1743 1914 2093
AltPolyRow3 k=0..3 T(3, k) n^kmissing0 -4 -44 -168 -424 -860 -1524 -2464 -3728 -5364 -7420 -9944 -12984 -16588 -20804 -25680 -31264
AltPolyCol2 k=0..n T(n, k) 2^kA0074661 -4 14 -44 128 -352 928 -2368 5888 -14336 34304 -80896 188416 -434176 991232 -2244608 5046272
AltPolyCol3 k=0..n T(n, k) 3^kmissing1 -6 33 -168 801 -3618 15633 -65124 263169 -1036638 3995649 -15116544 56273697 -206553402 748800369
AltPolyDiag k=0..n T(n, k) n^kA2773731 -2 14 -168 2840 -61870 1649232 -51988748 1891712384 -78031713690 3598075308800 -183396819358192
RevTriangleT(n, k), 0 ≤ k ≤ nmissing1 2 0 4 1 0 8 6 2 0 16 24 19 6 0 32 80 110 80 24 0 64 240 500 615 418 120 0 128 672 1960 3570 4046
RevAccsee docsmissing1 2 2 4 5 5 8 14 16 16 16 40 59 65 65 32 112 222 302 326 326 64 304 804 1419 1837 1957 1957 128 800
RevAccRevsee docsmissing1 0 2 0 1 5 0 2 8 16 0 6 25 49 65 0 24 104 214 294 326 0 120 538 1153 1653 1893 1957 0 720 3324
RevAntiDiagsee docsmissing1 2 4 0 8 1 16 6 0 32 24 2 64 80 19 0 128 240 110 6 256 672 500 80 0 512 1792 1960 615 24 1024 4608
RevDiffx1T(n, k) (k+1)missing1 2 0 4 2 0 8 12 6 0 16 48 57 24 0 32 160 330 320 120 0 64 480 1500 2460 2090 720 0 128 1344 5880
RevRowSum k=0..n T(n, k)A0005221 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805
RevEvenSum k=0..n T(n, k) even(k)missing1 2 4 10 35 166 982 6854 54805 493210 4932056 54252562 651030679 8463398750 118487582410
RevOddSum k=0..n T(n, k) odd(k)A0381550 0 1 6 30 160 975 6846 54796 493200 4932045 54252550 651030666 8463398736 118487582395
RevAltSum k=0..n T(n, k) (-1)^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
RevAbsSum k=0..n | T(n, k) |A0005221 2 5 16 65 326 1957 13700 109601 986410 9864101 108505112 1302061345 16926797486 236975164805
RevDiagSum k=0..n // 2 T(n - k, k)missing1 2 4 9 22 58 163 484 1508 4903 16564 57942 209269 778494 2976848 11679985 46950810 193094310
RevAccSum k=0..n j=0..k T(n, j)missing1 4 14 54 245 1320 8342 60774 502273 4646140 47573494 534284630 6530896869 86323201952
RevAccRevSum k=0..n j=0..k T(n, n - j)missing1 2 6 26 145 962 7314 62526 593737 6204370 70795718 876281826 11697961961 167578760338
RevRowLcmLcm k=0..n | T(n, k) | > 1missing1 2 4 24 912 5280 205656000 2528588160 5874643821231360 916835503928037603840
RevRowGcdGcd k=0..n | T(n, k) | > 1A0000341 2 4 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
RevRowMaxMax k=0..n | T(n, k) |missing1 2 4 8 24 110 615 4046 30604 261656 2579380 28167920 334925404 4308766176 59645959464 884178662640
RevColMiddleT(n, n // 2)missing1 2 1 6 19 110 615 3570 28777 167874 1769985 10369590 135131755 794409902 12330989671 72692509890
RevCentralET(2 n, n)missing1 1 19 615 28777 1769985 135131755 12330989671 1309509778577 158670146018241 21603959342147715
RevCentralOT(2 n + 1, n)missing2 6 110 3570 167874 10369590 794409902 72692509890 7737183602434 939252936527334 128086499559331950
RevColLeftT(n, 0)A0000791 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
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 2 6 32 250 2452 28294 372276 5476902 88843388 1572182524 30095481528 618922505656 13596524483960
RevInvBinConv k=0..n C(n, k) T(n, n - k) (-1)^kmissing1 -2 2 4 10 -52 -626 -3600 -4378 209092 3583684 37666352 228658456 -1320343832 -74742710402
RevTransNat0 k=0..n T(n, k) kmissing0 0 1 10 80 636 5357 48826 484136 5217960 60931617 767776714 10395900616 150651962852 2327754304605
RevTransNat1 k=0..n T(n, k) (k + 1)missing1 2 6 26 145 962 7314 62526 593737 6204370 70795718 876281826 11697961961 167578760338
RevTransSqrs k=0..n T(n, k) k^2missing0 0 1 14 154 1624 17463 196398 2336108 29522064 396817845 5669643550 85976013110 1381026109384
RevPosHalf k=0..n 2^n T(n, k) (1/2)^kA0819231 4 18 92 536 3552 26608 223456 2085504 21450752 241320704 2949474816 38933066752 552141672448
RevNegHalf k=0..n (-2)^n T(n, k) (-1/2)^kA0074661 -4 14 -44 128 -352 928 -2368 5888 -14336 34304 -80896 188416 -434176 991232 -2244608 5046272
RevDiagRow1T(n + 1, n)A0001422 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200
RevDiagRow2T(n + 2, n)missing4 6 19 80 418 2604 18828 154944 1429776 14620320 164089440 2005361280 26508781440 376870959360
RevDiagRow3T(n + 3, n)missing8 24 110 615 4046 30604 261656 2495340 26263512 302411736 3781675872 51039346176 739493351424
RevDiagCol1T(n + 1, 1)A0017880 1 6 24 80 240 672 1792 4608 11520 28160 67584 159744 372736 860160 1966080 4456448 10027008
RevDiagCol2T(n + 2, 2)missing0 2 19 110 500 1960 6944 22848 71040 211200 605440 1683968 4566016 12113920 31539200 80773120
RevDiagCol3T(n + 3, 3)missing0 6 80 615 3570 17360 74592 292320 1066560 3674880 12080640 38182144 116712960 346644480 1004093440
RevPolysee docsmissing1 2 1 4 2 1 8 5 2 1 16 16 6 2 1 32 65 28 7 2 1 64 326 188 44 8 2 1 128 1957 1656 421 64 9 2 1 256
RevPolyRow1 k=0..1 T(1, k) n^kA0556422 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
RevPolyRow2 k=0..2 T(2, k) n^kA0000274 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 38
RevPolyRow3 k=0..3 T(3, k) n^kA1378828 16 28 44 64 88 116 148 184 224 268 316 368 424 484 548 616 688 764 844 928 1016 1108 1204 1304
RevPolyCol2 k=0..n T(n, k) 2^kA0842621 2 6 28 188 1656 17992 232016 3460368 58574368 1109200736 23230928832 533139875776 13304094478208
RevPolyCol3 k=0..n T(n, k) 3^kA3462581 2 7 44 421 5366 84907 1601552 35052649 872931626 24368595631 753607111412 25572085243597
RevPolyDiag k=0..n T(n, k) n^kmissing1 2 6 44 800 28182 1627192 139512536 16635343104 2632245555050 533576186400224 134812040651954052
 << 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.