OFFSET
0,4
FORMULA
G.f.: Sum_{k>=0} x^k / (1 - k * x^2).
a(n) ~ sqrt(Pi) * (n/LambertW(exp(1)*n))^((n + 1 - n/LambertW(exp(1)*n))/2) / sqrt(1 + LambertW(exp(1)*n)). - Vaclav Kotesovec, Apr 14 2022
MATHEMATICA
Join[{1}, Table[Sum[(n-2k)^k, {k, 0, Floor[n/2]}], {n, 40}]] (* Harvey P. Dale, Dec 12 2022 *)
PROG
(PARI) a(n) = sum(k=0, n\2, (n-2*k)^k);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k*x^2)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 09 2022
STATUS
approved