A357965 Expansion of e.g.f. exp( (exp(x^4) - 1)/x^3 ).
1, 1, 1, 1, 1, 61, 361, 1261, 3361, 68041, 1073521, 8343721, 43290721, 432509221, 11472541081, 165124339381, 1457296102081, 12237047593681, 322364521392481, 7462073325643921, 103362225413048641, 1051987428484484941, 21127644716862970441
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((exp(x^4)-1)/x^3))) -
PARI
a(n) = n!*sum(k=0, n\4, stirling(n-3*k, n-4*k, 2)/(n-3*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(n/4)} Stirling2(n-3*k,n-4*k)/(n-3*k)!.