A376565 E.g.f. satisfies A(x) = exp( x*A(x) * (1 + x^3*A(x)^3) ).

1, 1, 3, 16, 149, 2016, 34447, 692224, 15986889, 420544000, 12494098331, 414681513984, 15201740343517, 609446038061056, 26511336043734375, 1243650774790045696, 62591481040666342673, 3364694927903114919936, 192423068815578523022899, 11665229364232192000000000

Offset: 0

Author

Seiichi Manyama, Sep 28 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A088695, A376564.

Cf. A190875, A376477.

Programs

PARI

a(n) = n!*sum(k=0, n\4, (n+1)^(n-3*k-1)*binomial(n-3*k, k)/(n-3*k)!);

Formula

E.g.f.: (1/x) * Series_Reversion( x*exp(-x * (1 + x^3)) ).

a(n) = n! * Sum_{k=0..floor(n/4)} (n+1)^(n-3*k-1) * binomial(n-3*k,k)/(n-3*k)!.