A367881 Expansion of e.g.f. 1/(1 - 3 * x * (exp(x) - 1)).

1, 0, 6, 9, 228, 1095, 23238, 215481, 4657992, 66216555, 1553967210, 29793656013, 777115661292, 18608934688383, 542832959656302, 15470567460571905, 503794462155308688, 16557037363336856019, 598704921471691072242, 22205328374455141122165

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

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

Prog

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

Crossrefs

Cf. A052848, A367880.

Sequence in context: A265383 A375661 A375672 * A367879 A377720 A377689

Adjacent sequences: A367878 A367879 A367880 * A367882 A367883 A367884

Keyword

nonn

Author

Seiichi Manyama, Dec 03 2023

Status

approved