OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..582
FORMULA
G.f.: Sum_{k>=0} (2*x)^k/(1 - k*x).
a(n) ~ sqrt(2*Pi/(1 + LambertW(exp(1)*n/2))) * n^(n + 1/2) * exp(n/LambertW(exp(1)*n/2) - n) / LambertW(exp(1)*n/2)^(n + 1/2). - Vaclav Kotesovec, Feb 06 2022
MATHEMATICA
a[0] = 1; a[n_] := Sum[2^k * k^(n-k), {k, 1, n}]; Array[a, 25, 0] (* Amiram Eldar, Feb 06 2022 *)
PROG
(PARI) a(n) = sum(k=0, n, 2^k*k^(n-k));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (2*x)^k/(1-k*x)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 06 2022
STATUS
approved