A365031 E.g.f. satisfies A(x) = exp(x * A(x) * (1 + x * A(x))^2).

1, 1, 7, 70, 1085, 22176, 569107, 17583616, 636085305, 26383168000, 1234691104031, 64368785424384, 3699873561469813, 232476344504965120, 15853643565560296875, 1166213594266747273216, 92052000392983157418353, 7760655405804462332903424

Offset: 0

Author

Seiichi Manyama, Aug 17 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..352
• Index entries for reversions of series

Crossrefs

Cf. A088695, A365032.

Cf. A364939.

Programs

Mathematica

Array[#!*Sum[ (# + 1)^(k - 1)*Binomial[2 k, # - k]/k!, {k, 0, #}] &, 18, 0] (* Michael De Vlieger, Aug 18 2023 *)

PARI

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

Formula

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

E.g.f.: (1/x) * Series_Reversion( x*exp(-x*(1 + x)^2) ). - Seiichi Manyama, Sep 23 2024