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%I #33 Sep 08 2022 08:46:18
%S 1,33,594,7667,79101,691119,5299019,36518791,230122266,1343028082,
%T 7331536586,37731144564,184232285897,857974579385,3827695162667,
%U 16420097827188,67948512704413,271990545250303,1055719283332541,3981884465793740,14621550982740229
%N Expansion of Product_{k>=1} (1 - x^(7*k))^32/(1 - x^k)^33 in powers of x.
%H Seiichi Manyama, <a href="/A282926/b282926.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{n>=1} (1 - x^(7*n))^32/(1 - x^n)^33.
%F a(n) ~ exp(Pi*sqrt(398*n/21)) * sqrt(199) / (4*sqrt(3) * 7^(33/2) * n). - _Vaclav Kotesovec_, Nov 10 2017
%t nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^32/(1 - x^k)^33, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *)
%o (PARI) my(m=30, x='x+O('x^m)); Vec(prod(j=1,m, (1 - x^(7*j))^32/(1 - x^j)^33)) \\ _G. C. Greubel_, Nov 18 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^32/(1 - x^j)^33: j in [1..m]]) )); // _G. C. Greubel_, Nov 18 2018
%o (Sage)
%o R = PowerSeriesRing(ZZ, 'x')
%o prec = 30
%o x = R.gen().O(prec)
%o s = prod((1 - x^(7*j))^32/(1 - x^j)^33 for j in (1..prec))
%o print(s.coefficients()) # _G. C. Greubel_, Nov 18 2018
%Y Cf. A282919.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 24 2017
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