A370710 a(n) = 3^n * [x^n] Product_{k>=1} 1/(1 - 3*x^k)^(1/3).

1, 3, 27, 180, 1431, 10206, 83025, 641277, 5264109, 42896790, 357649587, 2989185039, 25284805857, 214547921451, 1832454271926, 15702526829196, 135091225972926, 1165383100947105, 10081310266960155, 87401262194470719, 759320707197024909, 6608561546767471227, 57610976508944343963

Offset: 0

Author

Vaclav Kotesovec, Feb 27 2024

Keywords

• nonn

Crossrefs

Cf. A242587, A370712.

Programs

Mathematica

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

Formula

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

a(n) ~ c * 9^n / n^(2/3), where c = 1 / (Gamma(1/3) * QPochhammer(1/3)^(1/3)) = 0.45283708537555770181385241925945547307046394744...