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

%I #6 Feb 29 2024 06:23:50

%S 1,6,138,2292,47046,852756,18266628,366635112,7948637382,170568754692,

%T 3761729402412,83136335360856,1863229219846428,41883396293989320,

%U 948524060727094728,21555960625992644304,492036151405623971142,11264431786398948383844,258676355450246122857756

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

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

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

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

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

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

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 28 2024