A371020 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x^2/2*exp(x)) ).

1, 0, 1, 3, 18, 160, 1545, 19131, 273868, 4463460, 82561545, 1695986875, 38413504866, 951203750718, 25551218851249, 740338919242755, 23014265170565880, 764047265130952456, 26981593786255568913, 1009915667787285212787, 39938889756657408019390

Offset: 0

Author

Seiichi Manyama, Mar 08 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A370889.

Programs

PARI

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

PARI

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