OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..500
FORMULA
G.f.: Sum_{k>=0} x^k/(1 - 2*k * x).
a(n) ~ sqrt(Pi) * (2*n/LambertW(2*exp(1)*n))^(1/2 + n - n/LambertW(2*exp(1)*n)) / sqrt(1 + LambertW(2*exp(1)*n)). - Vaclav Kotesovec, Dec 07 2021
MATHEMATICA
a[n_] := Sum[If[k == n == 0, 1, (2*k)^(n - k)], {k, 0, n}]; Array[a, 24, 0] (* Amiram Eldar, Dec 07 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, (2*k)^(n-k));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-2*k*x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 07 2021
STATUS
approved