A384136 a(n) = (3*n)!/(2*n)! * Sum_{k=1..n} 1/(2*n+k).

1, 11, 191, 4578, 140274, 5238132, 230784840, 11720201616, 674092013040, 43310839531680, 3074579815271040, 238983481496188800, 20187063842072319360, 1841332369689189619200, 180372122189263722009600, 18885338733119777188300800, 2104722524872544008142592000

Offset: 1

Author

Seiichi Manyama, May 20 2025

Keywords

• nonn

Crossrefs

Cf. A098118, A384137.

Cf. A383678.

Programs

PARI

a(n) = sum(k=0, n, k*(2*n+1)^(k-1)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} k * (2*n+1)^(k-1) * |Stirling1(n,k)|.

a(n) = n! * [x^n] (-log(1 - x)/(1 - x)^(2*n+1)).