OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..429
FORMULA
G.f.: Sum_{k>=0} (k * x)^(2 * k) / (1 - k * x).
a(n) ~ exp((3 + (-1)^n)/2) * (n/2)^n / (exp(2) - 1). - Vaclav Kotesovec, Apr 14 2022
MATHEMATICA
a[0] = 1; a[n_] := Sum[k^n, {k, 0, Floor[n/2]}]; Array[a, 22, 0] (* Amiram Eldar, Apr 13 2022 *)
PROG
(PARI) a(n) = sum(k=0, n\2, k^n);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^(2*k)/(1-k*x)))
(Magma) [(&+[k^n: k in [0..Floor(n/2)]]): n in [0..40]]; // G. C. Greubel, Nov 01 2022
(SageMath) [sum( k^n for k in range((n//2)+1)) for n in range(41)] # G. C. Greubel, Nov 01 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 13 2022
STATUS
approved