A352981 a(n) = Sum_{k=0..floor(n/2)} k^n.

1, 0, 1, 1, 17, 33, 794, 2316, 72354, 282340, 10874275, 53201625, 2438235715, 14350108521, 762963987380, 5249352196144, 317685943157892, 2502137235710736, 169842891165484965, 1506994510201252425, 113394131858832552133, 1119223325228757961465

Offset: 0

Author

Seiichi Manyama, Apr 13 2022

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..429

Crossrefs

Cf. A089072, A104872, A352982, A352983.

Programs

Magma

[(&+[k^n: k in [0..Floor(n/2)]]): n in [0..40]]; // G. C. Greubel, Nov 01 2022

Mathematica

a[0] = 1; a[n_] := Sum[k^n, {k, 0, Floor[n/2]}]; Array[a, 22, 0] (* Amiram Eldar, Apr 13 2022 *)

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)))

SageMath

[sum( k^n for k in range((n//2)+1)) for n in range(41)] # G. C. Greubel, Nov 01 2022

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