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A356687 a(n) = n! * Sum_{k=0..n} k^(2*n)/k!. 3
1, 1, 18, 927, 94876, 16251045, 4210190766, 1543550310211, 764096247603480, 493254380867214249, 404269328278061434810, 411862088865696890314311, 512690851568229926690616948, 768775988931240685277619894157 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
E.g.f.: Sum_{k>=0} (k^2 * x)^k / (k! * (1 - k^2 * x)).
MATHEMATICA
a[n_] := n! * Sum[k^(2*n)/k!, {k, 0, n}]; a[0] = 1; Array[a, 14, 0] (* Amiram Eldar, Aug 23 2022 *)
PROG
(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)))))
CROSSREFS
Sequence in context: A214160 A242446 A160013 * A123786 A333089 A129009
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 23 2022
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)