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 A303342 #5 Apr 22 2018 03:09:58 %S A303342 1,6,72,1008,10746,130896,1569456,17371584,192625128,2260005462, %T A303342 24725148912,270748885392,3027318848208,32608207056528, %U A303342 354309508944288,3902606972751168,41393526342215994,443390745816982944,4783687280410092984,50532141192366275280 %N A303342 Expansion of Product_{k>=1} ((1 + (9*x)^k) / (1 - (9*x)^k))^(1/3). %C A303342 In general, for h>=1, if g.f. = Product_{k>=1} ((1 + (h^2*x)^k) / (1 - (h^2*x)^k))^(1/h), then a(n) ~ h^(2*n) * exp(Pi*sqrt(n/h)) / (2^(3/2 + 3/(2*h)) * h^(1/4 + 1/(4*h)) * n^(3/4 + 1/(4*h))). %F A303342 a(n) ~ 3^(2*n) * exp(Pi*sqrt(n/3)) / (4 * 3^(1/3) * n^(5/6)). %t A303342 nmax = 20; CoefficientList[Series[Product[((1+(9*x)^k)/(1-(9*x)^k))^(1/3), {k, 1, nmax}], {x, 0, nmax}], x] %Y A303342 Cf. A271236, A303074, A303307. %K A303342 nonn %O A303342 0,2 %A A303342 _Vaclav Kotesovec_, Apr 22 2018