A370734 a(n) = 8^n * [x^n] Product_{k>=1} 1/(1 - 3*x^k)^(1/4).

1, 6, 138, 2292, 47046, 852756, 18266628, 366635112, 7948637382, 170568754692, 3761729402412, 83136335360856, 1863229219846428, 41883396293989320, 948524060727094728, 21555960625992644304, 492036151405623971142, 11264431786398948383844, 258676355450246122857756

Offset: 0

Author

Vaclav Kotesovec, Feb 28 2024

Keywords

• nonn

Crossrefs

Cf. A242587 (m=1), A370714 (m=2), A370710 (m=3), A370735 (m=5).

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1-3*x^k), {k, 1, nmax}]^(1/4), {x, 0, nmax}], x] * 8^Range[0, nmax]
nmax = 20; CoefficientList[Series[Product[1/(1-3*(8*x)^k), {k, 1, nmax}]^(1/4), {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} 1/(1 - 3*(8*x)^k)^(1/4).

a(n) ~ 24^n / (Gamma(1/4) * QPochhammer(1/3)^(1/4) * n^(3/4)).