A360481 E.g.f. satisfies A(x) = x * exp(x + 2 * A(x)).

0, 1, 6, 63, 1044, 23805, 692118, 24482115, 1020584232, 49000005945, 2662853279850, 161586078510879, 10830019921469532, 794577001293803637, 63339899145968483262, 5451312770064188283195, 503784284643602483767632, 49757423537114340032969073

Offset

0,3

Links

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

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

Formula

E.g.f.: A(x) = -LambertW(-2*x * exp(x))/2.

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

a(n) ~ sqrt(1 + LambertW(exp(-1)/2)) * n^(n-1) / (2 * LambertW(exp(-1)/2)^n * exp(n)). - Vaclav Kotesovec, Feb 17 2023

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-2*x*exp(x))/2)))
(PARI) a(n) = sum(k=1, n, 2^(k-1)*k^(n-1)*binomial(n, k));

Crossrefs

Cf. A216857, A360482, A360483, A360484.

Cf. A360473.

Sequence in context: A280476 A295241 A271607 * A079244 A023815 A249590

Adjacent sequences: A360478 A360479 A360480 * A360482 A360483 A360484

Keyword

nonn

Author

Seiichi Manyama, Feb 09 2023

Status

approved