A350164 a(n) = Sum_{k=1..n}(-1)^(k+1) * floor(n/(2*k-1))^n.

1, 4, 26, 255, 3125, 46593, 823415, 16776960, 387400807, 9999941975, 285311495511, 8916083675135, 302875039491581, 11112006557122561, 437893859877597389, 18446743921164642176, 827240261123526320144, 39346407973736968327497

Offset: 1

Author

Seiichi Manyama, Dec 18 2021

Keywords

• nonn

Crossrefs

Main diagonal of A350161.

Cf. A101455, A344724, A350145, A350167.

Programs

Mathematica

a[n_] := Sum[(-1)^(k + 1) * Floor[n/(2*k - 1)]^n, {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Dec 18 2021 *)

PARI

a(n) = sum(k=1, n, (-1)^(k+1)*(n\(2*k-1))^n);

PARI

a(n) = sum(k=1, n, sumdiv(k, d, kronecker(-4, k/d)*(d^n-(d-1)^n)));

Formula

a(n) = Sum_{k=1..n} Sum_{d|k} A101455(k/d) * (d^n - (d - 1)^n).

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k/(1 + x^(2*k)).

a(n) ~ n^n. - Vaclav Kotesovec, Dec 18 2021