A370877 Expansion of e.g.f. (1/x) * Series_Reversion( x/(x + exp(x^2/2)) ).

1, 1, 3, 15, 111, 1095, 13605, 204225, 3597825, 72788625, 1663323795, 42373980495, 1190822561775, 36596898673335, 1221033470181525, 43954996792932225, 1698138394110583425, 70082689941923083425, 3077205709746516423075, 143235112906380591471375

Offset: 0

Author

Seiichi Manyama, Mar 03 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A352410, A370878.

Programs

PARI

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

PARI

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

Formula

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