A375588 Expansion of e.g.f. 1 / (1 + x - x * exp(x^2)).
1, 0, 0, 6, 0, 60, 720, 840, 40320, 378000, 2116800, 60207840, 598752000, 7792424640, 181863601920, 2288689603200, 45855781171200, 1016682053587200, 17113328962329600, 422970486434496000, 9765438564930048000, 213305542403822668800, 5916931500898517299200
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2)))) -
PARI
a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(k, n-2*k, 2)/k!);
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * Stirling2(k,n-2*k)/k!.