A382087 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^2) ), where B(x) = 1 + x*B(x)^3 is the g.f. of A001764.

1, 1, 7, 106, 2525, 82536, 3436867, 174045376, 10385025849, 713599868800, 55498397386751, 4819444051348224, 462246012357060373, 48531686994029295616, 5536163290789601602875, 681824639839489261060096, 90168540044259473683829873, 12744019609725371553920876544

Offset: 0

Author

Seiichi Manyama, Mar 15 2025

Keywords

• nonn

Crossrefs

Cf. A382086, A382088, A382089.

Cf. A001764, A377832, A382037.

Programs

PARI

a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(2*n+k-1, k)/(n-k-1)!));

Formula

E.g.f. A(x) satisfies A(x) = exp(x*A(x) * B(x*A(x))^2).

a(n) = (n-1)! * Sum_{k=0..n-1} (n+1)^(n-k-1) * binomial(2*n+k-1,k)/(n-k-1)! for n > 0.

E.g.f.: exp( Series_Reversion( x * (1-x)^2 * exp(-x) ) ).