A380664 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-x/(1 - x)^2) ).

1, 2, 17, 268, 6277, 196416, 7716109, 365398496, 20271580137, 1290027358720, 92653747607401, 7414981595716608, 654373744057368493, 63136350047908917248, 6612064512998173129125, 747016321343021395603456, 90564758322246657646854481, 11727981253987656671672008704

Offset: 0

Author

Seiichi Manyama, Jan 30 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A377831, A380663.

Cf. A361598.

Programs

PARI

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

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(2*n+k,n-k)/k!.