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 A370435 #9 Feb 27 2024 04:05:20
%S A370435 1,1,4,29,120,820,3625,23400,105000,669500,3075625,18837500,89237500,
%T A370435 532500000,2554062500,15086640625,72843750000,421773437500,
%U A370435 2084812500000,11834804687500,58638281250000,332210205078125,1656773437500000,9240966796875000,46624682617187500,257479980468750000
%N A370435 Expansion of Product_{n>=1} (1 - 5^(n-1)*x^n) * (1 + 5^(n-1)*x^n)^2.
%C A370435 Compare to Product_{n>=1} (1 - 5^n*x^n) * (1 + 5^n*x^n)^2 = Sum_{n>=0} 5^(n*(n+1)/2) * x^(n*(n+1)/2).
%H A370435 Paul D. Hanna, <a href="/A370435/b370435.txt">Table of n, a(n) for n = 0..630</a>
%F A370435 a(n) ~ c^(1/4) * 5^(n + 3/2) * exp(2*sqrt(c*n)) / (24 * sqrt(Pi) * n^(3/4)), where c = -2*polylog(2, -1/5) - polylog(2, 1/5). - _Vaclav Kotesovec_, Feb 27 2024
%e A370435 G.f.: A(x) = 1 + x + 4*x^2 + 29*x^3 + 120*x^4 + 820*x^5 + 3625*x^6 + 23400*x^7 + 105000*x^8 + 669500*x^9 + 3075625*x^10 + 18837500*x^11 + ...
%e A370435 where A(x) is the series expansion of the infinite product given by
%e A370435 A(x) = (1 - x)*(1 + x)^2 * (1 - 5*x^2)*(1 + 5*x^2)^2 * (1 - 25*x^3)*(1 + 25*x^3)^2 * (1 - 125*x^4)*(1 + 125*x^4)^2 * ... * (1 - 5^(n-1)*x^n)*(1 + 5^(n-1)*x^n)^2 * ...
%o A370435 (PARI) {a(n) = polcoeff( prod(k=1,n, (1 - 5^(k-1)*x^k) * (1 + 5^(k-1)*x^k)^2 +x*O(x^n)), n)}
%o A370435 for(n=0,40, print1(a(n),", "))
%Y A370435 Cf. A370337, A370338, A370434, A344064, A338674.
%K A370435 nonn
%O A370435 0,3
%A A370435 _Paul D. Hanna_, Feb 26 2024