A350167 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/(2*k-1))^k.

1, 2, 2, 3, 5, 3, 3, 4, 1, 9, 9, 3, 5, -9, 1, 2, 4, 25, 25, 63, -13, -75, -75, -89, -26, 102, 296, 122, 124, -58, -58, -57, -741, -229, -471, 288, 290, -732, 1302, 1472, 1474, 2824, 2824, -542, -4556, -8650, -8650, -8680, -9783, -1320, 17818, 32016, 32018, 20252, 9054, 7360

Offset: 1

Author

Seiichi Manyama, Dec 18 2021

Keywords

• sign

Links

• Winston de Greef, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A350147, A350164.

Programs

Mathematica

a[n_] := Sum[(-1)^(k + 1) * Floor[n/(2*k - 1)]^k, {k, 1, n}]; Array[a, 50] (* Amiram Eldar, Dec 18 2021 *)

PARI

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

PARI

my(N=66, x='x+O('x^N)); Vec(-sum(j=1, N, (1-x^(2*j-1))*sum(k=1, N, (-k)^j*x^(k*(2*j-1))))/(1-x))

Formula

G.f.: -(1/(1 - x)) * Sum_{j>=1} Sum{k>=1} (-k)^j * x^(k*(2*j-1)) * (1 - x^(2*j-1)).