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

%I #11 Dec 04 2023 06:35:25

%S 1,0,6,27,324,3645,54918,923643,18061704,394663833,9607469130,

%T 256997250279,7502660832780,237243300445125,8079508278302958,

%U 294800526215739315,11473728720705019152,474469344621574172721,20774758472643152149650

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

%F a(0) = 1; a(n) = n * Sum_{k=2..n} 3^(k-1) * binomial(n-1,k-1) * a(n-k).

%F a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-k) * k! * Stirling2(n-k,k)/(n-k)!.

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

%Y Cf. A052848, A367885.

%Y Cf. A337039, A351737.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 04 2023