A376564 E.g.f. satisfies A(x) = exp( x*A(x) * (1 + x^2*A(x)^2) ).

1, 1, 3, 22, 245, 3456, 60487, 1283584, 31971753, 912448000, 29369155211, 1053204332544, 41646891006877, 1800306963331072, 84464613778359375, 4274750510822588416, 232146299393990454353, 13465725621588464173056, 830921722002492358973203

Offset: 0

Author

Seiichi Manyama, Sep 28 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A088695, A376565.

Cf. A118395, A376476.

Programs

PARI

a(n) = n!*sum(k=0, n\3, (n+1)^(n-2*k-1)*binomial(n-2*k, k)/(n-2*k)!);

Formula

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

a(n) = n! * Sum_{k=0..floor(n/3)} (n+1)^(n-2*k-1) * binomial(n-2*k,k)/(n-2*k)!.