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A278558
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Expansion of Product_{n>=1} (1 - x^(5*n))^30/(1 - x^n)^31 in powers of x.
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11
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1, 31, 527, 6448, 63240, 526443, 3852742, 25380847, 153068700, 855816380, 4479330091, 22117432019, 103672066076, 463698703204, 1987628351600, 8195086588810, 32603090921532, 125497791966435, 468512597653134, 1699911932127300, 6005651320362628, 20693956328627358
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OFFSET
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0,2
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COMMENTS
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In general, if m>0 and g.f. = Product_{k>=1} (1 - x^(5*k))^m/(1 - x^k)^(m+1) then a(n) ~ sqrt(4*m+5) * exp(Pi*sqrt(2*(4*m+5)*n/15)) / (4*sqrt(3)*5^((m+1)/2)*n). - Vaclav Kotesovec, Nov 28 2016
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LINKS
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FORMULA
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G.f.: Product_{n>=1} (1 - x^(5*n))^30/(1 - x^n)^31.
a(n) ~ exp(Pi*5*sqrt(2*n/3)) / (24414062500*sqrt(3)*n). - Vaclav Kotesovec, Nov 28 2016
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MATHEMATICA
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nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))^30/(1 - x^k)^31, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 28 2016 *)
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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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