A371018 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x^2*exp(x)) ).

1, 0, 2, 6, 60, 620, 7950, 129402, 2365496, 50512968, 1208642490, 32223422990, 947694971652, 30435132773916, 1061061668979494, 39889366397571810, 1608910488000292080, 69305890226183224592, 3175519952912430375666, 154216789672147809137046

Offset: 0

Author

Seiichi Manyama, Mar 08 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A161633, A371019.

Cf. A365283.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x^2*exp(x)))/x))

PARI

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

Formula

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