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 A153737 A recursive triangular sequence with row sums (2*(n + 5)!): A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (n + 4)*(n + 3)*A(n - 2, k - 1). 0
 2, 5040, 5040, 2, 80636, 2, 2, 362878, 362878, 2, 2, 363024, 6531548, 363024, 2, 2, 363206, 39553592, 39553592, 363206, 2, 2, 363428, 79849438, 797577464, 79849438, 363428, 2, 2, 363694, 128156058, 6098501046, 6098501046, 128156058, 363694, 2, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are (2*(n + 5)!) except for n=1: {2, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600, 174356582400, 2615348736000}. LINKS FORMULA A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (n + 4)*(n + 3)*A(n - 2, k - 1). EXAMPLE {2}, {5040, 5040}, {2, 80636, 2}, {2, 362878, 362878, 2}, {2, 363024, 6531548, 363024, 2}, {2, 363206, 39553592, 39553592, 363206, 2}, {2, 363428, 79849438, 797577464, 79849438, 363428, 2}, {2, 363694, 128156058, 6098501046, 6098501046, 128156058, 363694, 2}, {2, 364008, 185214520, 18683169432, 136619086476, 18683169432, 185214520, 364008, 2}, {2, 364374, 251770836, 42192786508, 1265229446280, 1265229446280, 42192786508, 251770836, 364374, 2} MATHEMATICA Clear[A]; A[2, 1] := A[2, 2] = 7!; A[3, 2] = 2*8! - 4; A[4, 2] = A[4, 3] = 9! - 2; A[n_, 1] := 2; A[n_, n_] := 2; A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n + 4)*(n + 3)*A[n - 2, k - 1]; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a] Table[Apply[Plus, a[[n]]], {n, 1, 10}]; |Q Table[Apply[Plus, a[[n]]]/(2*(n + 5)!), {n, 1, 10}]; CROSSREFS Sequence in context: A203756 A232712 A262059 * A078933 A064029 A057645 Adjacent sequences:  A153734 A153735 A153736 * A153738 A153739 A153740 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Dec 31 2008 STATUS approved

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Last modified August 24 22:41 EDT 2019. Contains 326314 sequences. (Running on oeis4.)