A380779 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x / (1 + x)) / (1 + x)^2 ).

1, 3, 23, 298, 5529, 134496, 4062631, 146903184, 6193969137, 298577002240, 16204658051031, 978156957629952, 65017249611283657, 4719532271850590208, 371519503997940966375, 31526820740816885549056, 2869134152226896957509089, 278763390556764407051452416

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)) ) * (1 + x*A(x))^2.

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

Prog

(PARI) a(n, q=1, r=1, s=1, t=-1, u=2) = 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. A377829, A380778, A380780, A380781.

Cf. A380675.

Sequence in context: A343849 A307418 A365546 * A231788 A356872 A088692

Adjacent sequences: A380776 A380777 A380778 * A380780 A380781 A380782

Keyword

nonn

Author

Seiichi Manyama, Feb 02 2025

Status

approved