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 A153738 Adjusted recursive triangular sequence with row sums 2*(n+5)!/6!: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (n + 4)*(n + 3)*A(n - 2, k - 1). 0
 2, 7, 7, 1, 110, 1, 1, 503, 503, 1, 1, 576, 8926, 576, 1, 1, 667, 54772, 54772, 667, 1, 1, 778, 118799, 1091404, 118799, 778, 1, 1, 911, 207621, 8440107, 8440107, 207621, 911, 1, 1, 1068, 329900, 27180372, 187139238, 27180372, 329900, 1068, 1, 1, 1251 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are: {2, 14, 112, 1008, 10080, 110880, 1330560, 17297280, 242161920, 3632428800,...}. The division by 6! and changing the first element gives a nicer looking result. 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}, {7, 7}, {1, 110, 1}, {1, 503, 503, 1}, {1, 576, 8926, 576, 1}, {1, 667, 54772, 54772, 667, 1}, {1, 778, 118799, 1091404, 118799, 778, 1}, {1, 911, 207621, 8440107, 8440107, 207621, 911, 1}, {1, 1068, 329900, 27180372, 187139238, 27180372, 329900, 1068, 1}, {1, 1251, 496770, 65297294, 1750419084, 1750419084, 65297294, 496770, 1251, 1} MATHEMATICA Clear[A] A[1, 1] = 2*6!/720; A[2, 1] := A[2, 2] = 7!/720; A[3, 2] = (2*8! - 2*6!)/720; A[4, 2] = A[4, 3] = ( 9! - 6!)/720; A[n_, 1] := 6!/720; A[n_, n_] := 6!/720; 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}]; Table[Apply[Plus, 720*a[[n]]]/(2*(n + 5)!), {n, 1, 10}]; CROSSREFS Sequence in context: A155541 A021787 A011052 * A159790 A251809 A016639 Adjacent sequences:  A153735 A153736 A153737 * A153739 A153740 A153741 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Dec 31 2008 STATUS approved

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Last modified March 18 22:11 EDT 2019. Contains 321305 sequences. (Running on oeis4.)