A380762 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * (1 + x)^2) / (1 + x) ).

1, 2, 15, 208, 4249, 115656, 3946879, 162225680, 7807264497, 430828353280, 26825288214031, 1860715287986688, 142304071119852745, 11897080341213068288, 1079508321205459768575, 105660694801273960216576, 11097101798773200862180321, 1244852059489783737208012800

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies A(x) = exp( x * A(x) * (1 + x*A(x))^2 ) * (1 + x*A(x)).

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

Prog

(PARI) a(n, q=1, r=1, s=1, t=2, u=1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial(r*u*n+((s-r)*u+t)*k+q*u, n-k)/k!);

Crossrefs

Cf. A000129, A088690.

Cf. A365031, A380781.

Cf. A380664.

Sequence in context: A282521 A099718 A143881 * A380663 A377890 A298692

Adjacent sequences: A380756 A380757 A380758 * A380763 A380764 A380765

Keyword

nonn

Author

Seiichi Manyama, Feb 02 2025

Status

approved