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 A360191 #12 Mar 19 2023 14:40:41
%S A360191 1,5,18,55,149,371,867,1923,4086,8374,16634,32152,60669,112041,202943,
%T A360191 361200,632647,1091917,1859225,3126242,5195715,8541624,13899866,
%U A360191 22404091,35787815,56683294,89061028,138872410,214984454,330532633,504869316,766357010,1156355165
%N A360191 G.f. 1 / Product_{n>=1} (1 - x^n)^3 * (1 - x^(2*n-1))^2.
%C A360191 Self-convolution inverse of A080332.
%H A360191 Vaclav Kotesovec, <a href="/A360191/b360191.txt">Table of n, a(n) for n = 0..10000</a>
%F A360191 G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.
%F A360191 (!) A(x) = 1 / [Product_{n>=1} (1 - x^n)^3 * (1 - x^(2*n-1))^2].
%F A360191 (2) A(x) = 1 / [Sum_{n=-oo..+oo} (6*n + 1) * x^(n*(3*n + 1)/2)].
%F A360191 a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (12*sqrt(2)*n^(3/2)). - _Vaclav Kotesovec_, Feb 07 2023
%e A360191 G.f.: A(x) = 1 + 5*x + 18*x^2 + 55*x^3 + 149*x^4 + 371*x^5 + 867*x^6 + 1923*x^7 + 4086*x^8 + 8374*x^9 + 16634*x^10 + 32152*x^11 + 60669*x^12 + ...
%t A360191 nmax = 30; CoefficientList[Series[1/Product[(1 - x^k)^3 * (1 - x^(2*k-1))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 07 2023 *)
%t A360191 nmax = 30; CoefficientList[Series[1/(QPochhammer[x] * EllipticTheta[4, 0, x]^2), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 07 2023 *)
%o A360191 (PARI) {a(n) = polcoeff( 1/prod(m=1,n, (1 - x^m)^3 * (1 - x^(2*m-1))^2 +x*O(x^n)), n)}
%o A360191 for(n=0,32,print1(a(n),", "))
%Y A360191 Cf. A080332, A361535, A361050, A361550.
%K A360191 nonn
%O A360191 0,2
%A A360191 _Paul D. Hanna_, Jan 29 2023