A380673 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-x * (1 - x)) ).

1, 2, 11, 106, 1501, 28416, 677839, 19566128, 663801849, 25897000960, 1142424023731, 56232973813248, 3055417111781269, 181644488496644096, 11728204122824976375, 817281148114199197696, 61136484485752079320561, 4886365932210442324672512, 415573028022035962921316059

Offset: 0

Author

Seiichi Manyama, Jan 30 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A377831, A380663, A380664.

Cf. A277184.

Programs

PARI

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

Formula

E.g.f. A(x) satisfies A(x) = exp(x * A(x) * (1 - x*A(x)))/(1 - x*A(x)).

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

a(n) = A277184(n+1)/(n+1).