%I #10 Sep 03 2024 12:13:57

%S 1,5,45,565,9085,177925,4106445,109105365,3279219485,109983317925,

%T 4071784884845,164919693538165,7253726995805885,344284133391481925,

%U 17538600019076063245,954467594134586386965,55263075631036363208285,3391909484128563111709925

%N Expansion of e.g.f. 1 / (4 - 3 * exp(x))^(5/3).

%F a(n) = (1/2) * Sum_{k=0..n} A008544(k+1) * Stirling2(n,k).

%t nmax=17; CoefficientList[Series[1 / (4 - 3 * Exp[x])^(5/3),{x,0,nmax}],x]*Range[0,nmax]! (* _Stefano Spezia_, Sep 03 2024 *)

%o (PARI) a008544(n) = prod(k=0, n-1, 3*k+2);

%o a(n) = sum(k=0, n, a008544(k+1)*stirling(n, k, 2))/2;

%Y Cf. A032033, A346982, A365558, A375949.

%Y Cf. A008544.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 03 2024