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A356687
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a(n) = n! * Sum_{k=0..n} k^(2*n)/k!.
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3
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1, 1, 18, 927, 94876, 16251045, 4210190766, 1543550310211, 764096247603480, 493254380867214249, 404269328278061434810, 411862088865696890314311, 512690851568229926690616948, 768775988931240685277619894157
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: Sum_{k>=0} (k^2 * x)^k / (k! * (1 - k^2 * x)).
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MATHEMATICA
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a[n_] := n! * Sum[k^(2*n)/k!, {k, 0, n}]; a[0] = 1; Array[a, 14, 0] (* Amiram Eldar, Aug 23 2022 *)
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PROG
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(PARI) a(n) = n!*sum(k=0, n, k^(2*n)/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*x)^k/(k!*(1-k^2*x)))))
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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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