A362775 E.g.f. satisfies A(x) = exp( x/(1-x)^2 * A(x) ).

1, 1, 7, 70, 965, 17216, 379207, 9969772, 305154313, 10668593008, 419714689931, 18358646058644, 884070662867053, 46486344447041032, 2650567497877525423, 162908800485532424236, 10737607698626311094033, 755571950776792829919968

Offset: 0

Author

Seiichi Manyama, May 02 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A082579, A362776.

Cf. A052868, A361065.

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(n+k-1,n-k)/k!.

From Vaclav Kotesovec, Nov 10 2023: (Start)

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

a(n) ~ 2^(n + 1/2) * sqrt(1 + 4*exp(-1) - sqrt(1 + 4*exp(-1))) * n^(n-1) / ((-1 + sqrt(1 + 4*exp(-1)))^(3/2) * (1 + 2*exp(-1) - sqrt(1 + 4*exp(-1)))^(n - 1/2) * exp(2*n-1)). (End)