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A282931 Expansion of Product_{k>=1} (1 - x^(7*k))^52/(1 - x^k)^53 in powers of x.

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%I A282931 #31 Sep 08 2022 08:46:18
%S A282931 1,53,1484,29097,447426,5734918,63638001,627260142,5594403499,
%T A282931 45779730871,347453597091,2466970932027,16501339314082,
%U A282931 104588498225862,631215364345159,3642533720923593,20170341090888205,107511123136305075,553099301324196585
%N A282931 Expansion of Product_{k>=1} (1 - x^(7*k))^52/(1 - x^k)^53 in powers of x.
%H A282931 Seiichi Manyama, <a href="/A282931/b282931.txt">Table of n, a(n) for n = 0..1000</a>
%F A282931 G.f.: Product_{n>=1} (1 - x^(7*n))^52/(1 - x^n)^53.
%F A282931 a(n) ~ exp(Pi*sqrt(638*n/21)) * sqrt(319) / (4*sqrt(3) * 7^(53/2) * n). - _Vaclav Kotesovec_, Nov 10 2017
%t A282931 nmax = 20; CoefficientList[Series[Product[(1 - x^(7*k))^52/(1 - x^k)^53, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *)
%o A282931 (PARI) my(N=30,x='x+O('x^N)); Vec(prod(j=1,N, (1 - x^(7*j))^52/(1 - x^j)^53)) \\ _G. C. Greubel_, Nov 18 2018
%o A282931 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^52/(1 - x^j)^53: j in [1..30]]) )); // _G. C. Greubel_, Nov 18 2018
%o A282931 (Sage)
%o A282931 R = PowerSeriesRing(ZZ, 'x')
%o A282931 prec = 30
%o A282931 x = R.gen().O(prec)
%o A282931 s = prod((1 - x^(7*j))^52/(1 - x^j)^53 for j in (1..prec))
%o A282931 print(s.coefficients()) # _G. C. Greubel_, Nov 18 2018
%Y A282931 Cf. A282919.
%K A282931 nonn
%O A282931 0,2
%A A282931 _Seiichi Manyama_, Feb 24 2017