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.
%I A363022 #87 Jul 25 2023 17:29:18
%S A363022 0,1,-3,7,-10,13,-21,35,-39,36,-55,85,-78,71,-118,155,-136,130,-171,
%T A363022 232,-234,177,-253,389,-310,248,-390,455,-406,378,-465,651,-586,426,
%U A363022 -626,832,-666,533,-822,1040,-820,734,-903,1129,-1144,783,-1081,1637,-1197,961,-1414,1580,-1378
%N A363022 Expansion of Sum_{k>0} x^(2*k)/(1+x^k)^3.
%H A363022 Seiichi Manyama, <a href="/A363022/b363022.txt">Table of n, a(n) for n = 1..10000</a>
%F A363022 G.f.: Sum_{k>0} binomial(k,2) * (-x)^k/(1 - x^k).
%F A363022 a(n) = Sum_{d|n} (-1)^d * binomial(d,2) = (A002129(n) - A321543(n))/2.
%t A363022 a[n_] := DivisorSum[n, (-1)^# * Binomial[#, 2] &]; Array[a, 50] (* _Amiram Eldar_, Jul 25 2023 *)
%o A363022 (PARI) my(N=60, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(2*k)/(1+x^k)^3)))
%o A363022 (PARI) a(n) = sumdiv(n, d, (-1)^d*binomial(d, 2));
%Y A363022 Cf. A325940, A363598, A363613, A363614.
%Y A363022 Cf. A002129, A069153, A321543.
%K A363022 sign
%O A363022 1,3
%A A363022 _Seiichi Manyama_, Jun 11 2023