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