A357967 Expansion of e.g.f. exp( x * (exp(x^3) - 1) ).
1, 0, 0, 0, 24, 0, 0, 2520, 20160, 0, 604800, 19958400, 79833600, 259459200, 25427001600, 326918592000, 1046139494400, 44460928512000, 1333827855360000, 10306043229081600, 125024130975744000, 6386367771463680000, 101695303941783552000, 861733891296165888000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3)-1)))) -
PARI
a(n) = n!*sum(k=0, n\3, stirling(k, n-3*k, 2)/k!);
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} Stirling2(k,n-3*k)/k!.