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a(n) = 3^(2*n) * [x^n] Product_{k>=1} 1/(1 - 2*x^k)^(1/3).
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%I #8 Feb 28 2024 17:57:54

%S 1,6,126,1818,32130,452142,8006526,117619290,1999520154,31550881374,

%T 527781570174,8556328428786,145177242834330,2404855490356782,

%U 40907085509085750,691705559193384114,11840743106503713594,202344257179543757526,3487245860820904368822,60077736592697832105330

%N a(n) = 3^(2*n) * [x^n] Product_{k>=1} 1/(1 - 2*x^k)^(1/3).

%F G.f.: Product_{k>=1} 1/(1 - 2*(9*x)^k)^(1/3).

%F a(n) ~ c * 18^n / n^(2/3), where c = 1 / (Gamma(1/3) * QPochhammer(1/2)^(1/3)) = 0.564734286036917647642848904946237...

%t nmax = 25; CoefficientList[Series[Product[1/(1-2*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]

%t nmax = 25; CoefficientList[Series[Product[1/(1-2*(9*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x]

%t nmax = 25; CoefficientList[Series[(-1/QPochhammer[2,x])^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]

%Y Cf. A070933, A370716.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 27 2024