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Expansion of Product_{k>=1} 1 / (1 - 3*x^k)^2.
2

%I #7 Dec 13 2023 08:37:16

%S 1,6,33,150,636,2508,9501,34674,123369,429396,1469733,4959600,

%T 16545597,54662046,179124837,582893052,1885479918,6067245570,

%U 19435083054,62006825166,197128631562,624716063502,1974151076946,6222482535642,19567579430643,61403207075448

%N Expansion of Product_{k>=1} 1 / (1 - 3*x^k)^2.

%H Vaclav Kotesovec, <a href="/A266944/b266944.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ c * n * 3^n, where c = Product_{k>=1} 1/(1-1/3^k)^2 = 1/QPochhammer(1/3)^2 = 3.187340158492291107944103748176139... .

%t nmax = 40; CoefficientList[Series[Product[1/(1-3*x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A242587, A266943.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jan 06 2016