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%I #10 Aug 29 2024 11:24:47
%S 1,1,2,9,48,320,2580,24150,258720,3117744,41741280,614774160,
%T 9877412160,171923225760,3222634615200,64721762305200,
%U 1386495651340800,31558444491974400,760564843136017920,19348085890139086080,518103061345155686400,14567452481227893811200
%N Expansion of e.g.f. 1/(1 - (exp(x^2) - 1)/x).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * Stirling2(n-k,n-2*k)/(n-k)!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^2)-1)/x)))
%o (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(n-k, n-2*k, 2)/(n-k)!);
%Y Cf. A000670, A375796.
%Y Cf. A357962.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 29 2024