VOOZH about

URL: https://oeis.org/A384137

⇱ A384137 - OEIS

login
A384137
a(n) = (4*n)!/(3*n)! * Sum_{k=1..n} 1/(3*n+k).
3
1, 15, 362, 12122, 520024, 27216936, 1681732464, 119823343440, 9671547654720, 872215286083200, 86920331742115200, 9485402065890543360, 1124985637517264409600, 144084905450972444851200, 19819350850103541715507200, 2914041773775561429169612800, 456069533875430113486232985600
OFFSET
1,2
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)).
PROG
(PARI) a(n) = sum(k=0, n, k*(3*n+1)^(k-1)*abs(stirling(n, k, 1)));
CROSSREFS
Cf. A382349.
Sequence in context: A240197 A012486 A035020 * A087330 A035274 A324415
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 20 2025
STATUS
approved