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Expansion of e.g.f. 1 / (5 - 4 * exp(x))^(3/2).
1

%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