A370715 a(n) = 3^(2*n) * [x^n] Product_{k>=1} 1/(1 - 2*x^k)^(1/3).

1, 6, 126, 1818, 32130, 452142, 8006526, 117619290, 1999520154, 31550881374, 527781570174, 8556328428786, 145177242834330, 2404855490356782, 40907085509085750, 691705559193384114, 11840743106503713594, 202344257179543757526, 3487245860820904368822, 60077736592697832105330

Offset: 0

Author

Vaclav Kotesovec, Feb 27 2024

Keywords

• nonn

Crossrefs

Cf. A070933, A370716.

Programs

Mathematica

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

Formula

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

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