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A282930
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Expansion of Product_{k>=1} (1 - x^(7*k))^48/(1 - x^k)^49 in powers of x.
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2
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1, 49, 1274, 23275, 334425, 4015011, 41818315, 387605443, 3256150548, 25135003348, 180196297050, 1210028211210, 7663549175191, 46039891115155, 263630633610437, 1444741006154614, 7604013727493190, 38554851707435000, 188824087108333495, 895363849845490543, 4119191297378031000, 18420594133878904635, 80204828814019528689
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: Product_{n>=1} (1 - x^(7*n))^48/(1 - x^n)^49.
a(n) ~ exp(Pi*sqrt(590*n/21)) * sqrt(295) / (4*sqrt(3) * 7^(49/2) * n). - Vaclav Kotesovec, Nov 10 2017
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MATHEMATICA
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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 *)
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PROG
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(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
(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
(Sage)
R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^48/(1 - x^j)^49 for j in (1..prec))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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