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 A294749 #10 Nov 08 2017 11:17:31
%S A294749 1,1,0,4,4,9,15,22,52,65,129,190,335,534,814,1399,2074,3462,5135,8303,
%T A294749 12658,19562,30182,45542,70620,105034,161223,239532,362929,539252,
%U A294749 805320,1197589,1769483,2624604,3847755,5681787,8291848,12165978,17696362,25796820
%N A294749 Expansion of Product_{k>=1} (1 + x^(2*k - 1))^(k^2).
%C A294749 In general, if g.f. = Product_{k>=1} (1 + x^(2*k-1))^(c2*k^2 + c1*k + c0) and c2>0, then a(n) ~ exp(Pi*sqrt(2)/3 * (7*c2/15)^(1/4) * n^(3/4) + 3*(c1+c2) * Zeta(3) / (2*Pi^2) * sqrt(15*n/(7*c2)) + (Pi*(4*c0 + 2*c1 + c2) * (15/(7*c2))^(1/4) / (24*sqrt(2)) - 9*(c1+c2)^2 * Zeta(3)^2 * (15/(7*c2))^(5/4) / (2^(3/2) * Pi^5)) * n^(1/4) + 2025*(c1+c2)^3 * Zeta(3)^3 / (49 * c2^2 * Pi^8) - 15*(c1+c2) * (4*c0 + 2*c1 + c2) * Zeta(3) / (112 * c2 * Pi^2)) * (7/15)^(1/8) * 2^((c1+c2)/24 - 9/4) * c2^(1/8) / n^(5/8).
%H A294749 Vaclav Kotesovec, <a href="/A294749/b294749.txt">Table of n, a(n) for n = 0..5000</a>
%F A294749 a(n) ~ exp(Pi/3 * (7/15)^(1/4) * sqrt(2) * n^(3/4) + 3*Zeta(3) * sqrt(15*n/7) / (2*Pi^2) + (Pi * (15/7)^(1/4) / (24*sqrt(2)) - 9*Zeta(3)^2 * (15/7)^(5/4) / (2^(3/2) * Pi^5)) * n^(1/4) + 2025*Zeta(3)^3 / (49*Pi^8) - 15*Zeta(3) / (112*Pi^2)) * (7/15)^(1/8) / (2^(53/24) * n^(5/8)).
%t A294749 nmax = 50; CoefficientList[Series[Product[(1+x^(2*k-1))^(k^2), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A294749 Cf. A027998, A263140, A294750, A294755.
%K A294749 nonn
%O A294749 0,4
%A A294749 _Vaclav Kotesovec_, Nov 08 2017