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A022729 Expansion of Product_{m>=1} 1/(1 - m*q^m)^5. 2

%I

%S 1,5,25,100,375,1276,4155,12775,37935,108460,301533,815075,2153995,

%T 5567685,14123030,35183376,86259665,208293520,496100890,1166243015,

%U 2708878924,6220640495,14134118490,31792023545

%N Expansion of Product_{m>=1} 1/(1 - m*q^m)^5.

%H G. C. Greubel, <a href="/A022729/b022729.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp(5*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 07 2018

%t With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-5, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Jul 25 2018 *)

%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^-5)) \\ _G. C. Greubel_, Jul 25 2018

%o (MAGMA) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^5:m in [1..n]])); // _G. C. Greubel_, Jul 25 2018

%Y Column k=5 of A297328.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

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Last modified March 20 19:23 EDT 2019. Contains 321349 sequences. (Running on oeis4.)