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A022570
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Expansion of Product_{m>=1} (1+x^m)^5.
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3
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1, 5, 15, 40, 95, 206, 425, 835, 1575, 2880, 5121, 8885, 15095, 25165, 41240, 66562, 105945, 166480, 258560, 397235, 604162, 910325, 1359680, 2014235, 2961000, 4321283, 6263360, 9019555, 12908945, 18367805, 25990149, 36581200, 51228175, 71393555, 99037095, 136775685, 188091960
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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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a(n) ~ (5/3)^(1/4) * exp(Pi * sqrt(5*n/3)) / (16 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015
G.f.: exp(5*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018
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MATHEMATICA
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nmax=50; CoefficientList[Series[Product[(1+q^m)^5, {m, 1, nmax}], {q, 0, nmax}], q] (* Vaclav Kotesovec, Mar 05 2015 *)
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PROG
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(PARI) x='x+O('x^51); Vec(prod(m=1, 50, (1 + x^m)^5)) \\ Indranil Ghosh, Apr 03 2017
(Magma) Coefficients(&*[(1+x^m)^5:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 26 2018
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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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