OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 09 2023
STATUS
approved