A378090 E.g.f. satisfies A(x) = exp(x * (1-x)^2 * A(x)) / (1-x)^3.

1, 4, 23, 181, 1889, 25411, 427615, 8736337, 210911489, 5882285971, 186121646831, 6585885144697, 257640988064641, 11039620794801691, 514147575711741119, 25858553659455655201, 1396703647943164718081, 80633376290492591578147, 4954794080385073122030799

Offset

0,2

Links

Table of n, a(n) for n=0..18.

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

Formula

E.g.f.: exp( -LambertW(-x/(1-x)) )/(1-x)^3.

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

a(n) ~ n^(n-1) * (1 + exp(1))^(n + 7/2) / exp(n + 5/2). - Vaclav Kotesovec, Aug 05 2025

Mathematica

terms = 19; A[_] = 0; Do[A[x_] = Exp[x*(1-x)^2*A[x]]/(1-x)^3 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0, terms-1]! (* Stefano Spezia, Mar 24 2025 *)

Prog

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

Crossrefs

Cf. A323772, A352410, A378091.

Sequence in context: A056814 A058863 A383985 * A192840 A302189 A292971

Adjacent sequences: A378087 A378088 A378089 * A378091 A378092 A378093

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2024

Status

approved