A360596 Expansion of e.g.f. 1/( (1 - x) * (1 + LambertW(-2*x)) ).

1, 3, 22, 282, 5224, 126120, 3742704, 131612432, 5347866752, 246490091136, 12704900911360, 724072211436288, 45209213973292032, 3068872654856532992, 225023336997933996032, 17724257054969009940480, 1492513932494133333753856, 133800772458366199028023296

Offset

0,2

Links

Table of n, a(n) for n=0..17.

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

Formula

a(n) = n! * Sum_{k=0..n} (2*k)^k / k!.

a(0)=1; a(n) = n*a(n-1) + (2*n)^n.

a(n) ~ 2^(n+1) * n^n / (2 - exp(-1)). - Vaclav Kotesovec, Feb 13 2023

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/((1-x)*(1+lambertw(-2*x)))))
(PARI) a(n) = n!*sum(k=0, n, (2*k)^k/k!);
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+(2*i)^i); v;

Crossrefs

Cf. A062971, A277506, A277509.

Sequence in context: A352448 A141360 A162659 * A206801 A135862 A122778

Adjacent sequences: A360593 A360594 A360595 * A360597 A360598 A360599

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 13 2023

Status

approved