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A343898
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a(n) = Sum_{k=0..n} (k!)^3 * binomial(n,k).
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5
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1, 2, 11, 244, 14741, 1799366, 383827807, 130673579576, 66583061972009, 48379301165408266, 48265538214413425331, 64129741094923528310012, 110669722298686436099306941, 242891356723607474283206170574, 665950191893557715599111566813191, 2246102991406652396042587363523672896
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OFFSET
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0,2
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COMMENTS
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Binomial transform of (n!)^3.
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} (k!)^3 * x^k/(1 - x)^(k+1).
E.g.f.: exp(x) * Sum_{k>=0} (k!)^2 * x^k.
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MATHEMATICA
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a[n_] := Sum[(k!)^3 * Binomial[n, k], {k, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, May 05 2021 *)
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PROG
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(PARI) a(n) = sum(k=0, n, k!^3*binomial(n, k));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!^3*x^k/(1-x)^(k+1)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=0, N, k!^2*x^k)))
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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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