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 A153658 Triangle read by rows: A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (n + 1)*(n + 2)*A(n - 2, k - 1). 0
 2, 120, 120, 2, 1436, 2, 2, 5038, 5038, 2, 2, 5124, 70388, 5124, 2, 2, 5238, 357640, 357640, 5238, 2, 2, 5384, 731806, 5783216, 731806, 5384, 2, 2, 5566, 1208610, 38702622, 38702622, 1208610, 5566, 2, 2, 5788, 1806416, 120409892, 713559004 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are (2*(n + 3)!) except for n=1 which is 2: {2, 240, 1440, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600}. LINKS Table of n, a(n) for n=1..41. EXAMPLE {2}, {120, 120}, {2, 1436, 2}, {2, 5038, 5038, 2}, {2, 5124, 70388, 5124, 2}, {2, 5238, 357640, 357640, 5238, 2}, {2, 5384, 731806, 5783216, 731806, 5384, 2}, {2, 5566, 1208610, 38702622, 38702622, 1208610, 5566, 2}, {2, 5788, 1806416, 120409892, 713559004, 120409892, 1806416, 5788, 2}, {2, 6054, 2546916, 281752828, 5942715000, 5942715000, 281752828, 2546916, 6054, 2} MATHEMATICA Clear[A]; A[2, 1] := A[2, 2] = (5)!; A[3, 2] = 2*(6)! - 4; A[4, 2] = A[4, 3] = (7)! - 2; A[n_, 1] := 2; A[n_, n_] := 2; A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n + 1)*(n + 2)*A[n - 2, k - 1]; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a] Table[Apply[Plus, a[[n]]], {n, 1, 10}]; Table[Apply[Plus, a[[n]]]/(2*(n + 3)!), {n, 1, 10}] CROSSREFS Sequence in context: A221231 A243512 A165163 * A073785 A102355 A206355 Adjacent sequences: A153655 A153656 A153657 * A153659 A153660 A153661 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Dec 30 2008 EXTENSIONS Edited by N. J. A. Sloane, Jun 02 2009 STATUS approved

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Last modified February 28 00:59 EST 2024. Contains 370379 sequences. (Running on oeis4.)