A370714 - OEIS

%I #7 Feb 28 2024 17:59:35

%S 1,6,78,780,8790,90708,1015692,10964760,122893926,1370476932,

%T 15518261220,176063641512,2014426860540,23109736996680,

%U 266397931733208,3079014279154224,35695144493030022,414708043501061988,4828444403991450612,56314242827277224712,657855733949279381652

%N a(n) = 4^n * [x^n] Product_{k>=1} 1/(1 - 3*x^k)^(1/2).

%F G.f.: Product_{k>=1} 1/(1 - 3*(4*x)^k)^(1/2).

%F a(n) ~ 12^n / sqrt(Pi*QPochhammer(1/3)*n).

%t nmax = 25; CoefficientList[Series[Product[1/(1-3*x^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x] * 4^Range[0, nmax]

%t nmax = 25; CoefficientList[Series[Product[1/(1-3*(4*x)^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x]

%t nmax = 25; CoefficientList[Series[Sqrt[-2/QPochhammer[3,x]], {x, 0, nmax}], x] * 4^Range[0, nmax]

%Y Cf. A242587, A370711.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 27 2024