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%I #19 Sep 08 2022 08:44:46
%S 1,3,12,37,114,312,855,2178,5496,13302,31719,73482,168086,375984,
%T 830976,1805887,3880746,8225460,17262440,35809446,73621776,149875003,
%U 302635110,605861124,1204043358,2374645746
%N Expansion of Product_{m>=1} (1-m*q^m)^-3.
%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 3, g(n) = n. - _Seiichi Manyama_, Dec 29 2017
%H Seiichi Manyama, <a href="/A022727/b022727.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: exp(3*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)^-3, {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)^-3)) \\ _G. C. Greubel_, Jul 25 2018
%o (Magma) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^3:m in [1..n]])); // _G. C. Greubel_, Jul 25 2018
%Y Column k=3 of A297328.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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