A370085 Expansion of e.g.f. exp( Sum_{k>=1} (3*k)! * (x/6)^k/k ).

1, 1, 21, 3421, 2232361, 4047831801, 16492042429501, 131524059703672021, 1862832637043775536721, 43582296764832433769579761, 1592318494850388661944336320101, 86870590496672779178378519636679501, 6822481321458299127004125050236325798521

Offset: 0

Author

Seiichi Manyama, Feb 08 2024

Keywords

• nonn

Crossrefs

Cf. A158876, A370084.

Cf. A370087.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, (3*k)!*(x/6)^k/k))))

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} (3*k)! * a(n-k) / (6^k * (n-k)!).