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A375795
Expansion of e.g.f. 1/(1 - (exp(x^2) - 1)/x).
3
1, 1, 2, 9, 48, 320, 2580, 24150, 258720, 3117744, 41741280, 614774160, 9877412160, 171923225760, 3222634615200, 64721762305200, 1386495651340800, 31558444491974400, 760564843136017920, 19348085890139086080, 518103061345155686400, 14567452481227893811200
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * Stirling2(n-k,n-2*k)/(n-k)!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^2)-1)/x)))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(n-k, n-2*k, 2)/(n-k)!);
CROSSREFS
Cf. A357962.
Sequence in context: A354312 A052826 A358264 * A246759 A191005 A257544
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 29 2024
STATUS
approved