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 A370434 #9 Feb 27 2024 04:04:27
%S A370434 1,1,3,19,60,348,1216,6480,23040,121152,445696,2214912,8475648,
%T A370434 40796160,158564352,754302976,2949120000,13694926848,55180001280,
%U A370434 250151436288,1008079994880,4570684063744,18552497111040,82564035379200,339344829186048,1494986847682560,6161930523770880
%N A370434 Expansion of Product_{n>=1} (1 - 4^(n-1)*x^n) * (1 + 4^(n-1)*x^n)^2.
%C A370434 Compare to Product_{n>=1} (1 - 4^n*x^n) * (1 + 4^n*x^n)^2 = Sum_{n>=0} 4^(n*(n+1)/2) * x^(n*(n+1)/2).
%H A370434 Paul D. Hanna, <a href="/A370434/b370434.txt">Table of n, a(n) for n = 0..630</a>
%F A370434 a(n) ~ c^(1/4) * 2^(2*n + 2) * exp(2*sqrt(c*n)) / (5 * sqrt(3*Pi) * n^(3/4)), where c = -2*polylog(2, -1/4) - polylog(2, 1/4). - _Vaclav Kotesovec_, Feb 27 2024
%e A370434 G.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 60*x^4 + 348*x^5 + 1216*x^6 + 6480*x^7 + 23040*x^8 + 121152*x^9 + 445696*x^10 + 2214912*x^11 + 8475648*x^12 + ...
%e A370434 where A(x) is the series expansion of the infinite product given by
%e A370434 A(x) = (1 - x)*(1 + x)^2 * (1 - 4*x^2)*(1 + 4*x^2)^2 * (1 - 16*x^3)*(1 + 16*x^3)^2 * (1 - 64*x^4)*(1 + 64*x^4)^2 * ... * (1 - 4^(n-1)*x^n)*(1 + 4^(n-1)*x^n)^2 * ...
%o A370434 (PARI) {a(n) = polcoeff( prod(k=1,n, (1 - 4^(k-1)*x^k) * (1 + 4^(k-1)*x^k)^2 +x*O(x^n)), n)}
%o A370434 for(n=0,40, print1(a(n),", "))
%Y A370434 Cf. A370337, A370338, A370435, A344063, A338673.
%K A370434 nonn
%O A370434 0,3
%A A370434 _Paul D. Hanna_, Feb 26 2024