A365779 Expansion of e.g.f. (exp(3*x) / (2 - exp(3*x)))^(5/6).

1, 5, 40, 485, 8005, 167000, 4208815, 124321685, 4211029030, 160879089275, 6843065055565, 320707303240010, 16418976236493805, 911678466840015425, 54568877697813515440, 3502486366009459019585, 239968694065209235561705, 17479992665536553731764200

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} (-3)^(n-k) * (Product_{j=0..k-1} (6*j+5)) * Stirling2(n,k).

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

a(0) = 1; a(n) = 5*a(n-1) + Sum_{k=1..n-1} 3^k * binomial(n-1,k) * a(n-k).

Prog

(PARI) a(n) = sum(k=0, n, (-3)^(n-k)*prod(j=0, k-1, 6*j+5)*stirling(n, k, 2));

Crossrefs

Cf. A365778.

Sequence in context: A282476 A198247 A088695 * A145166 A113079 A211046

Adjacent sequences: A365776 A365777 A365778 * A365780 A365781 A365782

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2023

Status

approved