OFFSET
0,5
FORMULA
G.f.: Sum_{k>=0} x^(2 * k) / (1 - k^2 * x).
a(n) ~ sqrt(Pi/2) * (n/(2*LambertW(exp(1)*n/2)))^(2*n + 1/2 - 2*n/LambertW(exp(1)*n/2)) / sqrt(1 + LambertW(exp(1)*n/2)). - Vaclav Kotesovec, Apr 14 2022
MATHEMATICA
a[0] = 1; a[n_] := Sum[k^(2*(n - 2*k)), {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* Amiram Eldar, Apr 13 2022 *)
PROG
(PARI) a(n) = sum(k=0, n\2, k^(2*(n-2*k)));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/(1-k^2*x)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 13 2022
STATUS
approved