A367886 Expansion of e.g.f. 1/(1 - x * (exp(3*x) - 1)).

1, 0, 6, 27, 324, 3645, 54918, 923643, 18061704, 394663833, 9607469130, 256997250279, 7502660832780, 237243300445125, 8079508278302958, 294800526215739315, 11473728720705019152, 474469344621574172721, 20774758472643152149650

Offset: 0

Author

Seiichi Manyama, Dec 04 2023

Keywords

• nonn

Crossrefs

Cf. A052848, A367885.

Cf. A337039, A351737.

Programs

PARI

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

Formula

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

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