A357968 Expansion of e.g.f. exp( x * (exp(x^4) - 1) ).
1, 0, 0, 0, 0, 120, 0, 0, 0, 181440, 1814400, 0, 0, 1037836800, 43589145600, 217945728000, 0, 14820309504000, 1867358997504000, 30411275102208000, 101370917007360000, 425757851430912000, 140500090972200960000, 5385836820601036800000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^4)-1)))) -
PARI
a(n) = n!*sum(k=0, n\4, stirling(k, n-4*k, 2)/k!);
Formula
a(n) = n! * Sum_{k=0..floor(n/4)} Stirling2(k,n-4*k)/k!.