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A282931
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Expansion of Product_{k>=1} (1 - x^(7*k))^52/(1 - x^k)^53 in powers of x.
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2
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1, 53, 1484, 29097, 447426, 5734918, 63638001, 627260142, 5594403499, 45779730871, 347453597091, 2466970932027, 16501339314082, 104588498225862, 631215364345159, 3642533720923593, 20170341090888205, 107511123136305075, 553099301324196585
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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))^52/(1 - x^n)^53.
a(n) ~ exp(Pi*sqrt(638*n/21)) * sqrt(319) / (4*sqrt(3) * 7^(53/2) * n). - Vaclav Kotesovec, Nov 10 2017
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MATHEMATICA
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nmax = 20; CoefficientList[Series[Product[(1 - x^(7*k))^52/(1 - x^k)^53, {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))^52/(1 - x^j)^53)) \\ G. C. Greubel, Nov 18 2018
(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
(Sage)
R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^52/(1 - x^j)^53 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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