A380880 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x*exp(x)) ).
1, 3, 33, 657, 19317, 756663, 37153071, 2196991317, 152107121481, 12074764795947, 1081507189545219, 107911010079715857, 11871250914793342797, 1427601609871824349407, 186326851375925627135127, 26232637698244127999077677, 3962908338833364902518738449, 639433805204122165558890771027
Offset: 0
Keywords
Programs
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PARI
a(n) = 3*sum(k=0, n, k^(n-k)*(3*n+3)^(k-1)*binomial(n, k));
Formula
E.g.f. A(x) satisfies A(x) = exp(3 * x * A(x) * exp(x * A(x))).
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A380881.
a(n) = 3 * Sum_{k=0..n} k^(n-k) * (3*n+3)^(k-1) * binomial(n,k).