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%I #35 Sep 08 2022 08:46:18
%S 1,45,1080,18285,244260,2733804,26606745,230915656,1819708110,
%T 13198528010,89041203249,563420646090,3366705675744,19105222953420,
%U 103448715353372,536621238174195,2675953974595655,12866398610335149,59805282183021050,269356649381129943,1177903345233332970,5010462608512204473,20765528801742226455
%N Expansion of Product_{k>=1} (1 - x^(7*k))^44/(1 - x^k)^45 in powers of x.
%H Seiichi Manyama, <a href="/A282929/b282929.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{n>=1} (1 - x^(7*n))^44/(1 - x^n)^45.
%F a(n) ~ exp(Pi*sqrt(542*n/21)) * sqrt(271) / (4*sqrt(3) * 7^(45/2) * n). - _Vaclav Kotesovec_, Nov 10 2017
%p N:= 30:
%p gN:= mul((1-x^(7*n))^44/(1-x^n)^45,n=1..N):
%p S:=series(gN,x,N+1):
%p seq(coeff(S,x,n),n=1..N); # _Robert Israel_, Nov 18 2018
%t nmax = 30; CoefficientList[Series[Product[(1 - x^(7*k))^44/(1 - x^k)^45, {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))^44/(1 - x^j)^45)) \\ _G. C. Greubel_, Nov 18 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^44/(1 - x^j)^45: 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))^44/(1 - x^j)^45 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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