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A282930 Expansion of Product_{k>=1} (1 - x^(7*k))^48/(1 - x^k)^49 in powers of x.

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%I A282930 #31 Sep 08 2022 08:46:18
%S A282930 1,49,1274,23275,334425,4015011,41818315,387605443,3256150548,
%T A282930 25135003348,180196297050,1210028211210,7663549175191,46039891115155,
%U A282930 263630633610437,1444741006154614,7604013727493190,38554851707435000,188824087108333495,895363849845490543,4119191297378031000,18420594133878904635,80204828814019528689
%N A282930 Expansion of Product_{k>=1} (1 - x^(7*k))^48/(1 - x^k)^49 in powers of x.
%H A282930 Seiichi Manyama, <a href="/A282930/b282930.txt">Table of n, a(n) for n = 0..1000</a>
%F A282930 G.f.: Product_{n>=1} (1 - x^(7*n))^48/(1 - x^n)^49.
%F A282930 a(n) ~ exp(Pi*sqrt(590*n/21)) * sqrt(295) / (4*sqrt(3) * 7^(49/2) * n). - _Vaclav Kotesovec_, Nov 10 2017
%t A282930 nmax = 20; CoefficientList[Series[Product[(1 - x^(7*k))^48/(1 - x^k)^49, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 10 2017 *)
%o A282930 (PARI) my(N=30, x='x+O('x^N)); Vec(prod(j=1,N, (1 - x^(7*j))^48/(1 - x^j)^49)) \\ _G. C. Greubel_, Nov 18 2018
%o A282930 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1 - x^(7*j))^48/(1 - x^j)^49: j in [1..30]]) )); // _G. C. Greubel_, Nov 18 2018
%o A282930 (Sage)
%o A282930 R = PowerSeriesRing(ZZ, 'x')
%o A282930 prec = 30
%o A282930 x = R.gen().O(prec)
%o A282930 s = prod((1 - x^(7*j))^48/(1 - x^j)^49 for j in (1..prec))
%o A282930 print(s.coefficients()) # _G. C. Greubel_, Nov 18 2018
%Y A282930 Cf. A282919.
%K A282930 nonn
%O A282930 0,2
%A A282930 _Seiichi Manyama_, Feb 24 2017