OEIS Similars: A196347, A021012
| ↕ Type | ↕ Trait | ↕ Anum | ↕ Sequence |
|---|---|---|---|
| Std | TriangleT(n, k), 0 ≤ k ≤ n | A196347 | 1 1 1 2 4 2 6 18 18 6 24 96 144 96 24 120 600 1200 1200 600 120 720 4320 10800 14400 10800 4320 720 |
| Std | RevT(n, n - k), 0 ≤ k ≤ n | A196347 | 1 1 1 2 4 2 6 18 18 6 24 96 144 96 24 120 600 1200 1200 600 120 720 4320 10800 14400 10800 4320 720 |
| Std | Accsee docs | missing | 1 1 2 2 6 8 6 24 42 48 24 120 264 360 384 120 720 1920 3120 3720 3840 720 5040 15840 30240 41040 |
| Std | AccRevsee docs | missing | 1 1 2 2 6 8 6 24 42 48 24 120 264 360 384 120 720 1920 3120 3720 3840 720 5040 15840 30240 41040 |
| Std | AntiDiagsee docs | missing | 1 1 2 1 6 4 24 18 2 120 96 18 720 600 144 6 5040 4320 1200 96 40320 35280 10800 1200 24 362880 |
| Std | Diffx1T(n, k) (k+1) | missing | 1 1 2 2 8 6 6 36 54 24 24 192 432 384 120 120 1200 3600 4800 3000 720 720 8640 32400 57600 54000 |
| Std | RowSum∑ k=0..n T(n, k) | A000165 | 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Std | EvenSum∑ k=0..n T(n, k) even(k) | A002866 | 1 1 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 |
| Std | OddSum∑ k=0..n T(n, k) odd(k) | A002866 | 0 1 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 |
| Std | AltSum∑ k=0..n T(n, k) (-1)^k | A000007 | 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 0 |
| Std | AbsSum∑ k=0..n | T(n, k) | | A000165 | 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Std | DiagSum∑ k=0..n // 2 T(n - k, k) | A240172 | 1 1 3 10 44 234 1470 10656 87624 806280 8211000 91707120 1114793280 14653936080 207138844080 |
| Std | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A187735 | 1 3 16 120 1152 13440 184320 2903040 51609600 1021870080 22295347200 531372441600 13733933875200 |
| Std | AccRevSum∑ k=0..n ∑ j=0..k T(n, n - j) | A187735 | 1 3 16 120 1152 13440 184320 2903040 51609600 1021870080 22295347200 531372441600 13733933875200 |
| Std | RowLcmLcm k=0..n | T(n, k) | > 1 | A360283 | 1 1 4 18 288 1200 43200 529200 11289600 91445760 9144576000 92207808000 13277924352000 |
| Std | RowGcdGcd k=0..n | T(n, k) | > 1 | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | RowMaxMax k=0..n | T(n, k) | | A059837 | 1 1 4 18 144 1200 14400 176400 2822400 45722880 914457600 18441561600 442597478400 10685567692800 |
| Std | ColMiddleT(n, n // 2) | A059837 | 1 1 4 18 144 1200 14400 176400 2822400 45722880 914457600 18441561600 442597478400 10685567692800 |
| Std | CentralET(2 n, n) | A122747 | 1 4 144 14400 2822400 914457600 442597478400 299195895398400 269276305858560000 |
| Std | CentralOT(2 n + 1, n) | A360602 | 1 18 1200 176400 45722880 18441561600 10685567692800 8414884558080000 8646761377013760000 |
| Std | ColLeftT(n, 0) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | ColRightT(n, n) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Std | BinConv∑ k=0..n C(n, k) T(n, k) | A001813 | 1 2 12 120 1680 30240 665280 17297280 518918400 17643225600 670442572800 28158588057600 |
| Std | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A122747 | 1 0 -4 0 144 0 -14400 0 2822400 0 -914457600 0 442597478400 0 -299195895398400 0 269276305858560000 |
| Std | TransNat0∑ k=0..n T(n, k) k | A014479 | 0 1 8 72 768 9600 138240 2257920 41287680 836075520 18579456000 449622835200 11771943321600 |
| Std | TransNat1∑ k=0..n T(n, k) (k + 1) | A187735 | 1 3 16 120 1152 13440 184320 2903040 51609600 1021870080 22295347200 531372441600 13733933875200 |
| Std | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 1 12 144 1920 28800 483840 9031680 185794560 4180377600 102187008000 2697737011200 76517631590400 |
| Std | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A032031 | 1 3 18 162 1944 29160 524880 11022480 264539520 7142567040 214277011200 7071141369600 |
| Std | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A000142 | 1 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200 |
| Std | DiagRow1T(n + 1, n) | A001563 | 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 |
| Std | DiagRow2T(n + 2, n) | A001804 | 2 18 144 1200 10800 105840 1128960 13063680 163296000 2195424000 31614105600 485707622400 |
| Std | DiagRow3T(n + 3, n) | A001805 | 6 96 1200 14400 176400 2257920 30481920 435456000 6586272000 105380352000 1780927948800 |
| Std | DiagCol1T(n + 1, 1) | A001563 | 1 4 18 96 600 4320 35280 322560 3265920 36288000 439084800 5748019200 80951270400 1220496076800 |
| Std | DiagCol2T(n + 2, 2) | A001804 | 2 18 144 1200 10800 105840 1128960 13063680 163296000 2195424000 31614105600 485707622400 |
| Std | DiagCol3T(n + 3, 3) | A001805 | 6 96 1200 14400 176400 2257920 30481920 435456000 6586272000 105380352000 1780927948800 |
| Std | Polysee docs | missing | 1 1 1 2 2 1 6 8 3 1 24 48 18 4 1 120 384 162 32 5 1 720 3840 1944 384 50 6 1 5040 46080 29160 6144 |
| Std | PolyRow1∑ k=0..1 T(1, k) n^k | 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 28 29 30 31 32 33 34 35 36 |
| Std | PolyRow2∑ k=0..2 T(2, k) n^k | A001105 | 2 8 18 32 50 72 98 128 162 200 242 288 338 392 450 512 578 648 722 800 882 968 1058 1152 1250 1352 |
| Std | PolyRow3∑ k=0..3 T(3, k) n^k | A244726 | 6 48 162 384 750 1296 2058 3072 4374 6000 7986 10368 13182 16464 20250 24576 29478 34992 41154 |
| Std | PolyCol2∑ k=0..n T(n, k) 2^k | A032031 | 1 3 18 162 1944 29160 524880 11022480 264539520 7142567040 214277011200 7071141369600 |
| Std | PolyCol3∑ k=0..n T(n, k) 3^k | A047053 | 1 4 32 384 6144 122880 2949120 82575360 2642411520 95126814720 3805072588800 167423193907200 |
| Std | PolyDiag∑ k=0..n T(n, k) n^k | A152684 | 1 2 18 384 15000 933120 84707280 10569646080 1735643790720 362880000000000 94121726392108800 |
| Alt | TriangleT(n, k), 0 ≤ k ≤ n | A196347 | 1 1 -1 2 -4 2 6 -18 18 -6 24 -96 144 -96 24 120 -600 1200 -1200 600 -120 720 -4320 10800 -14400 |
| Alt | RevT(n, n - k), 0 ≤ k ≤ n | A196347 | 1 -1 1 2 -4 2 -6 18 -18 6 24 -96 144 -96 24 -120 600 -1200 1200 -600 120 720 -4320 10800 -14400 |
| Alt | Accsee docs | missing | 1 1 0 2 -2 0 6 -12 6 0 24 -72 72 -24 0 120 -480 720 -480 120 0 720 -3600 7200 -7200 3600 -720 0 |
| Alt | AntiDiagsee docs | missing | 1 1 2 -1 6 -4 24 -18 2 120 -96 18 720 -600 144 -6 5040 -4320 1200 -96 40320 -35280 10800 -1200 24 |
| Alt | RowSum∑ k=0..n T(n, k) | A000007 | 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 0 |
| Alt | EvenSum∑ k=0..n T(n, k) even(k) | A002866 | 1 1 4 24 192 1920 23040 322560 5160960 92897280 1857945600 40874803200 980995276800 25505877196800 |
| Alt | OddSum∑ k=0..n T(n, k) odd(k) | A002866 | 0 -1 -4 -24 -192 -1920 -23040 -322560 -5160960 -92897280 -1857945600 -40874803200 -980995276800 |
| Alt | AltSum∑ k=0..n T(n, k) (-1)^k | A000165 | 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Alt | AbsSum∑ k=0..n | T(n, k) | | A000165 | 1 2 8 48 384 3840 46080 645120 10321920 185794560 3715891200 81749606400 1961990553600 |
| Alt | DiagSum∑ k=0..n // 2 T(n - k, k) | A013999 | 1 1 1 2 8 42 258 1824 14664 132360 1326120 14606640 175448160 2282469840 31972303440 479793807360 |
| Alt | AccSum∑ k=0..n ∑ j=0..k T(n, j) | A019590 | 1 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 |
| Alt | RowLcmLcm k=0..n | T(n, k) | > 1 | A360283 | 1 1 4 18 288 1200 43200 529200 11289600 91445760 9144576000 92207808000 13277924352000 |
| Alt | RowGcdGcd k=0..n | T(n, k) | > 1 | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | RowMaxMax k=0..n | T(n, k) | | A059837 | 1 1 4 18 144 1200 14400 176400 2822400 45722880 914457600 18441561600 442597478400 10685567692800 |
| Alt | ColMiddleT(n, n // 2) | A059837 | 1 1 -4 -18 144 1200 -14400 -176400 2822400 45722880 -914457600 -18441561600 442597478400 |
| Alt | CentralET(2 n, n) | A122747 | 1 -4 144 -14400 2822400 -914457600 442597478400 -299195895398400 269276305858560000 |
| Alt | CentralOT(2 n + 1, n) | A360602 | 1 -18 1200 -176400 45722880 -18441561600 10685567692800 -8414884558080000 8646761377013760000 |
| Alt | ColLeftT(n, 0) | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | ColRightT(n, n) | A000142 | 1 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200 |
| Alt | BinConv∑ k=0..n C(n, k) T(n, k) | A122747 | 1 0 -4 0 144 0 -14400 0 2822400 0 -914457600 0 442597478400 0 -299195895398400 0 269276305858560000 |
| Alt | InvBinConv∑ k=0..n C(n, k) T(n, n - k) (-1)^k | A001813 | 1 -2 12 -120 1680 -30240 665280 -17297280 518918400 -17643225600 670442572800 -28158588057600 |
| Alt | TransNat0∑ k=0..n T(n, k) k | A063524 | 0 -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 |
| Alt | TransSqrs∑ k=0..n T(n, k) k^2 | missing | 0 -1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
| Alt | PosHalf∑ k=0..n 2^n T(n, k) (1/2)^k | A000142 | 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 |
| Alt | NegHalf∑ k=0..n (-2)^n T(n, k) (-1/2)^k | A032031 | 1 -3 18 -162 1944 -29160 524880 -11022480 264539520 -7142567040 214277011200 -7071141369600 |
| Alt | DiagRow1T(n + 1, n) | A001563 | 1 -4 18 -96 600 -4320 35280 -322560 3265920 -36288000 439084800 -5748019200 80951270400 |
| Alt | DiagRow2T(n + 2, n) | A001804 | 2 -18 144 -1200 10800 -105840 1128960 -13063680 163296000 -2195424000 31614105600 -485707622400 |
| Alt | DiagRow3T(n + 3, n) | A001805 | 6 -96 1200 -14400 176400 -2257920 30481920 -435456000 6586272000 -105380352000 1780927948800 |
| Alt | DiagCol1T(n + 1, 1) | A001563 | -1 -4 -18 -96 -600 -4320 -35280 -322560 -3265920 -36288000 -439084800 -5748019200 -80951270400 |
| Alt | DiagCol2T(n + 2, 2) | A001804 | 2 18 144 1200 10800 105840 1128960 13063680 163296000 2195424000 31614105600 485707622400 |
| Alt | DiagCol3T(n + 3, 3) | A001805 | -6 -96 -1200 -14400 -176400 -2257920 -30481920 -435456000 -6586272000 -105380352000 -1780927948800 |
| Alt | Polysee docs | missing | 1 1 1 2 0 1 6 0 -1 1 24 0 2 -2 1 120 0 -6 8 -3 1 720 0 24 -48 18 -4 1 5040 0 -120 384 -162 32 -5 1 |
| Alt | PolyRow1∑ k=0..1 T(1, k) n^k | A000027 | 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 -26 |
| Alt | PolyRow2∑ k=0..2 T(2, k) n^k | A001105 | 2 0 2 8 18 32 50 72 98 128 162 200 242 288 338 392 450 512 578 648 722 800 882 968 1058 1152 1250 |
| Alt | PolyRow3∑ k=0..3 T(3, k) n^k | A244726 | 6 0 -6 -48 -162 -384 -750 -1296 -2058 -3072 -4374 -6000 -7986 -10368 -13182 -16464 -20250 -24576 |
| Alt | PolyCol2∑ k=0..n T(n, k) 2^k | A000142 | 1 -1 2 -6 24 -120 720 -5040 40320 -362880 3628800 -39916800 479001600 -6227020800 87178291200 |
| Alt | PolyCol3∑ k=0..n T(n, k) 3^k | A000165 | 1 -2 8 -48 384 -3840 46080 -645120 10321920 -185794560 3715891200 -81749606400 1961990553600 |
| Alt | PolyDiag∑ k=0..n T(n, k) n^k | missing | 1 0 2 -48 1944 -122880 11250000 -1410877440 232436776320 -48704929136640 12652843234348800 |
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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.