cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A350167 #21 Jun 30 2024 21:46:02
%S A350167 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 A350167 296,122,124,-58,-58,-57,-741,-229,-471,288,290,-732,1302,1472,1474,
%U A350167 2824,2824,-542,-4556,-8650,-8650,-8680,-9783,-1320,17818,32016,32018,20252,9054,7360
%N A350167 a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/(2*k-1))^k.
%H A350167 Winston de Greef, <a href="/A350167/b350167.txt">Table of n, a(n) for n = 1..1500</a>
%F A350167 G.f.: -(1/(1 - x)) * Sum_{j>=1} Sum{k>=1} (-k)^j * x^(k*(2*j-1)) * (1 - x^(2*j-1)).
%t A350167 a[n_] := Sum[(-1)^(k + 1) * Floor[n/(2*k - 1)]^k, {k, 1, n}]; Array[a, 50] (* _Amiram Eldar_, Dec 18 2021 *)
%o A350167 (PARI) a(n) = sum(k=1, n, (-1)^(k+1)*(n\(2*k-1))^k);
%o A350167 (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 A350167 Cf. A350147, A350164.
%K A350167 sign
%O A350167 1,2
%A A350167 _Seiichi Manyama_, Dec 18 2021