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%I #34 Sep 08 2022 08:46:18
%S 1,37,740,10545,119510,1142338,9548849,71529474,488650453,3084466705,
%T 18173253703,100751920597,529029597362,2645187324766,12651654794629,
%U 58105915432081,257102694583806,1099122519498352,4551159872375703,18293134887547452
%N Expansion of Product_{k>=1} (1 - x^(7*k))^36/(1 - x^k)^37 in powers of x.
%H Seiichi Manyama, <a href="/A282927/b282927.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{n>=1} (1 - x^(7*n))^36/(1 - x^n)^37.
%F a(n) ~ exp(Pi*sqrt(446*n/21)) * sqrt(223) / (4*sqrt(3) * 7^(37/2) * n). - _Vaclav Kotesovec_, Nov 10 2017
%t nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^36/(1 - x^k)^37, {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))^36/(1 - x^j)^37)) \\ _G. C. Greubel_, Nov 18 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^36/(1 - x^j)^37: 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))^36/(1 - x^j)^37 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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