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A282923 Expansion of Product_{n>=1} (1 - x^(7*n))^20/(1 - x^n)^21 in powers of x.

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%I A282923 #24 Sep 08 2022 08:46:18
%S A282923 1,21,252,2233,16170,100926,560945,2837398,13265679,57989435,
%T A282923 239125579,936702879,3505361650,12590400326,43572202835,145770820937,
%U A282923 472764167939,1490002933265,4573182416677,13694526423445,40076281579264,114782535792335,322167257486123,887188897987819,2399619923361150,6380874322337452,16695968482412345
%N A282923 Expansion of Product_{n>=1} (1 - x^(7*n))^20/(1 - x^n)^21 in powers of x.
%H A282923 Seiichi Manyama, <a href="/A282923/b282923.txt">Table of n, a(n) for n = 0..1000</a>
%F A282923 G.f.: Product_{n>=1} (1 - x^(7*n))^20/(1 - x^n)^21.
%F A282923 a(n) ~ exp(Pi*sqrt(254*n/21)) * sqrt(127) / (4*sqrt(3) * 7^(21/2) * n). - _Vaclav Kotesovec_, Nov 10 2017
%t A282923 nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^20/(1 - x^k)^21, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *)
%o A282923 (PARI) my(x='x+O('x^30)); Vec(prod(j=1, 30, (1 - x^(7*j))^20/(1 - x^j)^21)) \\ _G. C. Greubel_, Nov 18 2018
%o A282923 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^20/(1 - x^j)^21: j in [1..30]]) )); // _G. C. Greubel_, Nov 18 2018
%o A282923 (Sage)
%o A282923 R = PowerSeriesRing(ZZ, 'x')
%o A282923 prec = 30
%o A282923 x = R.gen().O(prec)
%o A282923 s = prod((1 - x^(7*j))^20/(1 - x^j)^21 for j in (1..prec))
%o A282923 print(s.coefficients()) # _G. C. Greubel_, Nov 18 2018
%Y A282923 Cf. A282919.
%K A282923 nonn
%O A282923 0,2
%A A282923 _Seiichi Manyama_, Feb 24 2017