A372333 Expansion of e.g.f. -exp(x) * LambertW(-2*x)/2.

0, 1, 6, 51, 684, 12965, 317298, 9500631, 336237016, 13729172553, 635237632350, 32844916975739, 1876755685038468, 117437155609780461, 7986793018367861194, 586578825469711599135, 46268265552518066488752, 3901008402618593931019409

Offset: 0

Author

Seiichi Manyama, Apr 28 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..352
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A277473, A372334.

Cf. A360548, A372315.

Programs

PARI

my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-exp(x)*lambertw(-2*x)/2)))

PARI

a(n) = sum(k=1, n, (2*k)^(k-1)*binomial(n, k));

Formula

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

G.f.: Sum_{k>=1} (2*k)^(k-1) * x^k / (1-x)^(k+1).

a(n) ~ exp(exp(-1)/2) * 2^(n-1) * n^(n-1). - Vaclav Kotesovec, Apr 30 2024