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A022637
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Expansion of Product_{m>=1} (1 + m*q^m)^9.
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2
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1, 9, 54, 273, 1197, 4761, 17577, 60957, 200799, 633007, 1920510, 5633667, 16037700, 44439840, 120165858, 317762553, 823240341, 2092864401, 5228118701, 12848849154, 31100190048, 74208885351, 174708121455, 406132690635, 932871440739, 2118595079790, 4759875472491
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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.: exp(9*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018
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MATHEMATICA
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With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^9, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 17 2018 *)
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PROG
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(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1+n*q^n)^9)) \\ G. C. Greubel, Feb 17 2018
(Magma) Coefficients(&*[(1+m*x^m)^9:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 17 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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