A362772 E.g.f. satisfies A(x) = exp( x * (1+x)^2 * A(x) ).

1, 1, 7, 58, 725, 11816, 239047, 5794972, 163861609, 5299694704, 193052158091, 7823764856084, 349236133422013, 17028109232138824, 900544754206010383, 51348494205747851116, 3140366001277974883793, 205067625446428300157408

Offset: 0

Author

Seiichi Manyama, May 02 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A000272, A362771.

Programs

PARI

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

Formula

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

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