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%I #32 Sep 08 2022 08:46:18
%S 1,29,464,5365,49880,394632,2750969,17296732,99742368,534126988,
%T 2681856693,12722233068,57373155952,247218913828,1022189562610,
%U 4070289420139,15656921120982,58336024110584,211023516790156,742643172981206,2547265600634862,8529351700138885
%N Expansion of Product_{k>=1} (1 - x^(7*k))^28/(1 - x^k)^29 in powers of x.
%H Seiichi Manyama, <a href="/A282925/b282925.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{n>=1} (1 - x^(7*n))^28/(1 - x^n)^29.
%F a(n) ~ exp(Pi*sqrt(350*n/21)) * sqrt(175) / (4*sqrt(3) * 7^(29/2) * n). - _Vaclav Kotesovec_, Nov 10 2017
%t nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^28/(1 - x^k)^29, {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))^28/(1 - x^j)^29)) \\ _G. C. Greubel_, Nov 18 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^28/(1 - x^j)^29: j in [1..m+2]]) )); // _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))^28/(1 - x^j)^29 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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