%I #11 Sep 06 2024 06:31:31

%S 1,4,32,368,5520,102064,2242832,57095728,1652211600,53559908784,

%T 1922581295632,75700072208688,3243905700776080,150289130386531504,

%U 7485459789379535632,398857142195958963248,22639650637589839298960,1363772478150606703714224

%N Expansion of e.g.f. 1 / (4 - 3 * exp(x))^(4/3).

%F a(n) = Sum_{k=0..n} A007559(k+1) * Stirling2(n,k).

%F a(n) ~ 3 * sqrt(Pi) * n^(n + 5/6) / (2^(13/6) * Gamma(1/3) * log(4/3)^(n + 4/3) * exp(n)). - _Vaclav Kotesovec_, Sep 06 2024

%t nmax=17; CoefficientList[Series[1 / (4 - 3 * Exp[x])^(4/3),{x,0,nmax}],x]*Range[0,nmax]! (* _Stefano Spezia_, Sep 03 2024 *)

%o (PARI) a007559(n) = prod(k=0, n-1, 3*k+1);

%o a(n) = sum(k=0, n, a007559(k+1)*stirling(n, k, 2));

%Y Cf. A032033, A346982, A365558, A375952.

%Y Cf. A005649, A007559, A375948.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 03 2024