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 A291316 #8 Dec 18 2023 12:11:03
%S A291316 1,1,1,2,0,1,3,-1,1,2,0,2,1,0,-1,4,2,-1,2,-3,4,3,-1,2,0,1,1,2,-2,2,5,
%T A291316 2,-3,0,1,-1,6,0,4,-2,-1,3,-1,2,0,4,-2,2,4,-2,1,5,-2,-2,-2,3,6,1,3,-2,
%U A291316 4,-3,-1,-2,3,6,2,0,-4,5,1,3,-1,0,0,4,-1,-2,4
%N A291316 Expansion of x/(1-x) + x^4*(1-x)/(1-x^3) + x^7*(1-x)*(1-x^3)/(1-x^5) + ... in powers of x.
%H A291316 George E. Andrews, <a href="https://georgeandrews1.github.io/pdf/320.pdf">The Bhargava-Adiga Summation and Partitions</a>, 2016. See equation (1.5)
%F A291316 a(n) = A008443(n) - A290735(n) = A290737(n) - A143064(n).
%e A291316 G.f. = x + x^2 + x^3 + 2*x^4 + x^6 + 3*x^7 - x^8 + x^9 + 2*x^10 + ...
%o A291316 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); A = sum(k=0, (n-1)\3, x^(3*k+1) * prod(i=1,k, 1 - x^(2*i-1), 1 + A) / (1 - x^(2*k+1)) ); polcoeff(A, n))};
%Y A291316 Cf. A008443, A143064, A290735, A290737.
%K A291316 sign
%O A291316 1,4
%A A291316 _Michael Somos_, Aug 22 2017