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%I #32 Sep 08 2022 08:46:18
%S 1,13,104,637,3276,14820,60697,229360,810498,2705118,8592857,26134654,
%T 76476816,216174700,592220696,1576826355,4090222409,10357895639,
%U 25653139694,62235901689,148108568986,346176981673,795569268689,1799508071426,4009753651904,8808973137510
%N Expansion of Product_{k>=1} (1 - x^(7*k))^12/(1 - x^k)^13 in powers of x.
%H Seiichi Manyama, <a href="/A282921/b282921.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{n>=1} (1 - x^(7*n))^12/(1 - x^n)^13.
%F a(n) ~ exp(Pi*sqrt(158*n/21)) * sqrt(79) / (4*sqrt(3) * 7^(13/2) * n). - _Vaclav Kotesovec_, Nov 10 2017
%t nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^12/(1 - x^k)^13, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *)
%o (PARI) my(N=30, x='x+O('x^N)); Vec(prod(j=1, N, (1 - x^(7*j))^12/(1 - x^j)^13)) \\ _G. C. Greubel_, Nov 18 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^12/(1 - x^j)^13: j in [1..30]]) )); // _G. C. Greubel_, Nov 18 2018
%o (Sage)
%o m = 30
%o R = PowerSeriesRing(ZZ, 'x')
%o x = R.gen().O(m)
%o s = prod((1 - x^(7*j))^12/(1 - x^j)^13 for j in (1..m))
%o list(s) # _G. C. Greubel_, Nov 18 2018
%Y Cf. A282919.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 24 2017
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