A377629 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x))^4 ).
1, 4, 60, 1644, 66712, 3611620, 245284344, 20071928212, 1923688610400, 211438912978692, 26225665058289640, 3624147718351890004, 552229557439437084816, 91990834731657653530180, 16632301623786709606057368, 3243982650658692575922907860, 678932992008068232965498759104
Offset: 0
Keywords
Programs
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PARI
a(n) = 4*n!*sum(k=0, n, k^(n-k)*binomial(4*n+k+4, k)/((4*n+k+4)*(n-k)!));
Formula
E.g.f. satisfies A(x) = 1/(1 - x * A(x) * exp(x*A(x)))^4.
E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377631.
a(n) = 4 * n! * Sum_{k=0..n} k^(n-k) * binomial(4*n+k+4,k)/( (4*n+k+4)*(n-k)! ).