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A337002
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a(n) = n! * Sum_{k=0..n} k^4 / k!.
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7
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0, 1, 18, 135, 796, 4605, 28926, 204883, 1643160, 14795001, 147960010, 1627574751, 19530917748, 253901959285, 3554627468406, 53319412076715, 853110593292976, 14502880086064113, 261051841549259010, 4959984989436051511, 99199699788721190220
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OFFSET
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0,3
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COMMENTS
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Exponential convolution of fourth powers (A000583) and factorial numbers (A000142).
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LINKS
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FORMULA
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E.g.f.: x * (1 + 7*x + 6*x^2 + x^3) * exp(x) / (1 - x).
a(0) = 0; a(n) = n * (n^3 + a(n-1)).
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MATHEMATICA
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Table[n! Sum[k^4/k!, {k, 0, n}], {n, 0, 20}]
nmax = 20; CoefficientList[Series[x (1 + 7 x + 6 x^2 + x^3) Exp[x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 0; a[n_] := a[n] = n (n^3 + a[n - 1]); Table[a[n], {n, 0, 20}]
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PROG
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(PARI) a(n) = n! * sum(k=0, n, k^4/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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