A384170 a(n) = 3^n * n! * binomial(5*n/3,n) * Sum_{k=1..n} 1/(2*n+3*k).

1, 17, 423, 14198, 603194, 31069980, 1882538440, 131223122480, 10345975290000, 910393948446560, 88452245803947200, 9405081915991747200, 1086351888729412883200, 135456246872643979788800, 18134220756665496528460800, 2594357788916663689703168000, 395006034401484168868002560000

Offset: 1

Author

Seiichi Manyama, May 21 2025

Keywords

• nonn

Crossrefs

Cf. A384136.

Programs

PARI

a(n) = sum(k=0, n, k*(2*n+3)^(k-1)*3^(n-k)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} k * (2*n+3)^(k-1) * 3^(n-k) * |Stirling1(n,k)|.

a(n) = n! * [x^n] ( -log(1 - 3*x)/(3 * (1 - 3*x)^(2*n/3+1)) ).