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A282929
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Expansion of Product_{k>=1} (1 - x^(7*k))^44/(1 - x^k)^45 in powers of x.
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2
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1, 45, 1080, 18285, 244260, 2733804, 26606745, 230915656, 1819708110, 13198528010, 89041203249, 563420646090, 3366705675744, 19105222953420, 103448715353372, 536621238174195, 2675953974595655, 12866398610335149, 59805282183021050, 269356649381129943, 1177903345233332970, 5010462608512204473, 20765528801742226455
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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))^44/(1 - x^n)^45.
a(n) ~ exp(Pi*sqrt(542*n/21)) * sqrt(271) / (4*sqrt(3) * 7^(45/2) * n). - Vaclav Kotesovec, Nov 10 2017
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MAPLE
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N:= 30:
gN:= mul((1-x^(7*n))^44/(1-x^n)^45, n=1..N):
S:=series(gN, x, N+1):
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MATHEMATICA
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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 *)
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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))^44/(1 - x^j)^45)) \\ G. C. Greubel, Nov 18 2018
(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
(Sage)
R = PowerSeriesRing(ZZ, 'x')
prec = 30
x = R.gen().O(prec)
s = prod((1 - x^(7*j))^44/(1 - x^j)^45 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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