A375592 Expansion of e.g.f. exp( x * (exp(x^3/6) - 1) ).
1, 0, 0, 0, 4, 0, 0, 70, 560, 0, 2800, 92400, 369600, 200200, 19619600, 252252000, 695094400, 5717712000, 171531360000, 1307259553600, 4852431584000, 136882025280000, 2175699958432000, 12698089211808000, 150837908212992000, 3848134863773200000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3/6)-1)))) -
PARI
a(n) = n!*sum(k=0, n\3, stirling(k, n-3*k, 2)/(6^k*k!));
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} Stirling2(k,n-3*k)/(6^k*k!).