%I #10 Sep 03 2024 12:14:13
%S 1,6,66,1026,20586,505746,14698506,493198866,18762818826,797986018386,
%T 37518173169546,1932228677052306,108176937646278666,
%U 6541409475478588626,424885004809917954186,29502494166061176035346,2180808897487960097444106
%N Expansion of e.g.f. 1 / (5 - 4 * exp(x))^(3/2).
%F a(n) = Sum_{k=0..n} A000407(k) * Stirling2(n,k).
%t nmax=16; CoefficientList[Series[1 / (5 - 4 * Exp[x])^(3/2),{x,0,nmax}],x]*Range[0,nmax]! (* _Stefano Spezia_, Sep 03 2024 *)
%o (PARI) a000407(n) = (2*n+1)!/n!;
%o a(n) = sum(k=0, n, a000407(k)*stirling(n, k, 2));
%Y Cf. A000407, A354242, A375947.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Sep 03 2024