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A337001
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a(n) = n! * Sum_{k=0..n} k^3 / k!.
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10
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0, 1, 10, 57, 292, 1585, 9726, 68425, 547912, 4931937, 49320370, 542525401, 6510306540, 84633987217, 1184875823782, 17773137360105, 284370197765776, 4834293362023105, 87017280516421722, 1653328329812019577, 33066566596240399540, 694397898521048399601
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OFFSET
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0,3
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COMMENTS
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Exponential convolution of cubes (A000578) and factorial numbers (A000142).
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LINKS
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FORMULA
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E.g.f.: x * (1 + 3*x + x^2) * exp(x) / (1 - x).
a(0) = 0; a(n) = n * (n^2 + a(n-1)).
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MATHEMATICA
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Table[n! Sum[k^3/k!, {k, 0, n}], {n, 0, 21}]
nmax = 21; CoefficientList[Series[x (1 + 3 x + x^2) Exp[x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 0; a[n_] := a[n] = n (n^2 + a[n - 1]); Table[a[n], {n, 0, 21}]
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PROG
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(PARI) a(n) = n! * sum(k=0, n, k^3/k!); \\ Michel Marcus, Aug 12 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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