A350167 - OEIS

%I #21 Jun 30 2024 21:46:02

%S 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,

%T 296,122,124,-58,-58,-57,-741,-229,-471,288,290,-732,1302,1472,1474,

%U 2824,2824,-542,-4556,-8650,-8650,-8680,-9783,-1320,17818,32016,32018,20252,9054,7360

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

%H Winston de Greef, <a href="/A350167/b350167.txt">Table of n, a(n) for n = 1..1500</a>

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

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

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

%o (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))

%Y Cf. A350147, A350164.

%K sign

%O 1,2

%A _Seiichi Manyama_, Dec 18 2021