OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..681
FORMULA
a(n) = Sum_{k=0..floor(n/2)} k^(n-2*k).
G.f.: Sum_{k>=0} x^(2*k) / (1 - k * x). - Seiichi Manyama, Apr 09 2022
a(n) ~ sqrt(Pi) * (n/(2*LambertW(exp(1)*n/2)))^(n + 1/2 - n/LambertW(exp(1)*n/2)) / sqrt(1 + LambertW(exp(1)*n/2)). - Vaclav Kotesovec, Apr 14 2022
PROG
(PARI) a(n) = sum(k=0, n\2, k^(n-2*k)); \\ Seiichi Manyama, Apr 09 2022
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/(1-k*x))) \\ Seiichi Manyama, Apr 09 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 28 2005
STATUS
approved