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 A329801 #8 Jan 15 2025 16:43:06
%S A329801 1,-1,2,-1,1,-1,1,-1,2,0,1,-3,1,-1,3,-1,1,-1,1,-2,3,-1,1,-3,1,-1,2,0,
%T A329801 1,-1,1,-1,2,-1,1,-2,1,-1,2,-2,1,-2,1,-1,4,-1,1,-3,1,0,2,-1,1,-1,2,-2,
%U A329801 2,-1,1,-5,1,-1,3,-1,1,0,1,-1,2,0,1,-4,1,-1,3,-1,1,0,1,-2,2,-1,1,-3,1
%N A329801 Expansion of Sum_{k>=1} x^(k*(k + 1)/2) / (1 + x^(k*(k + 1)/2)).
%H A329801 Antti Karttunen, <a href="/A329801/b329801.txt">Table of n, a(n) for n = 1..20000</a>
%F A329801 G.f.: Sum_{k>=1} (-1)^(k + 1) * theta_2(x^(k/2)) / (2 * x^(k/8)).
%F A329801 a(n) = Sum_{d|n} (-1)^(n/d + 1) * A010054(d).
%t A329801 nmax = 85; CoefficientList[Series[Sum[x^(k (k + 1)/2)/(1 + x^(k (k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A329801 Table[Sum[(-1)^(n/d + 1) Boole[IntegerQ[Sqrt[8 d + 1]]], {d, Divisors[n]}], {n, 1, 85}]
%o A329801 (PARI) A329801(n) = sumdiv(n,d,((-1)^(1+(n/d))) * ispolygonal(d,3)); \\ _Antti Karttunen_, Jan 15 2025
%Y A329801 Cf. A000217, A007862, A010054, A048272, A304876, A317529.
%K A329801 sign
%O A329801 1,3
%A A329801 _Ilya Gutkovskiy_, Nov 21 2019