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A022730 Expansion of Product_{m>=1} 1/(1 - m*q^m)^6. 2

%I

%S 1,6,33,146,594,2196,7687,25410,80664,246258,728610,2093334,5865853,

%T 16057998,43063812,113293158,292928448,745216692,1867840830,

%U 4616732712,11264133069,27149243724,64691795178

%N Expansion of Product_{m>=1} 1/(1 - m*q^m)^6.

%H G. C. Greubel, <a href="/A022730/b022730.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp(6*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)^-6, {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)^-6)) \\ _G. C. Greubel_, Jul 25 2018

%o (MAGMA) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^6:m in [1..n]])); // _G. C. Greubel_, Jul 25 2018

%Y Column k=6 of A297328.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

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Last modified February 17 10:59 EST 2019. Contains 320219 sequences. (Running on oeis4.)