A384137 a(n) = (4*n)!/(3*n)! * Sum_{k=1..n} 1/(3*n+k).

1, 15, 362, 12122, 520024, 27216936, 1681732464, 119823343440, 9671547654720, 872215286083200, 86920331742115200, 9485402065890543360, 1124985637517264409600, 144084905450972444851200, 19819350850103541715507200, 2914041773775561429169612800, 456069533875430113486232985600

Offset: 1

Author

Seiichi Manyama, May 20 2025

Keywords

• nonn

Crossrefs

Cf. A098118, A384136.

Cf. A382349.

Programs

PARI

a(n) = sum(k=0, n, k*(3*n+1)^(k-1)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} k * (3*n+1)^(k-1) * |Stirling1(n,k)|.

a(n) = n! * [x^n] (-log(1 - x)/(1 - x)^(3*n+1)).