A368293 - OEIS

%I #6 Dec 20 2023 12:37:01

%S 1,3,16,137,1572,22457,384934,7699449,176004376,4526214641,

%T 129331581954,4065059876033,139385578253524,5177627842411065,

%U 207123084913936174,8877473910719477033,405862594146337680816,19715036609777115714401,1014004150296746677804666

%N Expansion of e.g.f. exp(2*x) / (1 - x*exp(3*x)).

%F a(n) = n! * Sum_{k=0..n} (3*(n-k)+2)^k / k!.

%o (PARI) a(n) = n!*sum(k=0, n, (3*(n-k)+2)^k/k!);

%Y Cf. A336948, A368292.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Dec 19 2023