A357335 E.g.f. satisfies A(x) = (exp(x) - 1) * exp(2 * A(x)).

0, 1, 5, 49, 757, 16081, 435477, 14345297, 556857973, 24894290257, 1259621627349, 71165987957329, 4440821632449077, 303338709537825105, 22512353926895739797, 1803812930088064925265, 155195078834104237961717, 14270228623788585753803089

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.: -LambertW(2 * (1 - exp(x)))/2.

a(n) = Sum_{k=1..n} (2 * k)^(k-1) * Stirling2(n,k).

a(n) ~ sqrt(1 + 2*exp(1)) * n^(n-1) / (2 * exp(n) * log(1 + exp(-1)/2)^(n - 1/2)). - Vaclav Kotesovec, Nov 14 2022

Prog

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

Crossrefs

Cf. A048802, A357336.

Cf. A349524, A356000.

Sequence in context: A145088 A301386 A192557 * A290755 A062995 A293847

Adjacent sequences: A357332 A357333 A357334 * A357336 A357337 A357338

Keyword

nonn

Author

Seiichi Manyama, Sep 24 2022

Status

approved