A375562 Expansion of e.g.f. 1 / (1 + x * log(1 - x^3)).
1, 0, 0, 0, 24, 0, 0, 2520, 40320, 0, 1209600, 39916800, 479001600, 1556755200, 79913433600, 1961511552000, 25107347865600, 296406190080000, 11204153985024000, 263564384219136000, 4284610758844416000, 95795516571955200000, 3345240261242880000000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^3)))) -
PARI
a(n) = n!*sum(k=0, n\3, (n-3*k)!*abs(stirling(k, n-3*k, 1))/k!);
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)! * |Stirling1(k,n-3*k)|/k!.