A376492 E.g.f. satisfies A(x) = exp(x^2 * (1 + x) * A(x)^2).

1, 0, 2, 6, 60, 600, 7680, 123480, 2212560, 47053440, 1104092640, 29200802400, 845985349440, 26864561243520, 924556913280000, 34334318184566400, 1367790957223891200, 58194757879908249600, 2633788044958380710400, 126340003102675832870400

Offset: 0

Author

Seiichi Manyama, Sep 25 2024

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362771, A376493.

Cf. A376476.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x^2*(1+x))/2)))

PARI

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

Formula

E.g.f.: exp( -LambertW(-2*x^2 * (1+x))/2 ).

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