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Expansion of Product_{m>=1} (1 + m*q^m)^9.
2

%I #12 Sep 08 2022 08:44:46

%S 1,9,54,273,1197,4761,17577,60957,200799,633007,1920510,5633667,

%T 16037700,44439840,120165858,317762553,823240341,2092864401,

%U 5228118701,12848849154,31100190048,74208885351,174708121455,406132690635,932871440739,2118595079790,4759875472491

%N Expansion of Product_{m>=1} (1 + m*q^m)^9.

%H G. C. Greubel, <a href="/A022637/b022637.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp(9*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 08 2018

%t With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^9, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Feb 17 2018 *)

%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^9)) \\ _G. C. Greubel_, Feb 17 2018

%o (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

%Y Column k=9 of A297321.

%K nonn

%O 0,2

%A _N. J. A. Sloane_