A384169 a(n) = 4^n * n! * binomial(5*n/4,n) * Sum_{k=1..n} 1/(n+4*k).

1, 16, 347, 9856, 349269, 14885760, 742589175, 42479124480, 2742327328905, 197267905658880, 15649214440432275, 1357388618032742400, 127808331929417605725, 12983375200126773657600, 1415428114244995252270575, 164837363498660501913600000, 20423530465926352502482292625

Offset: 1

Author

Seiichi Manyama, May 21 2025

Keywords

• nonn

Crossrefs

Cf. A098118, A384167, A384168.

Cf. A303487.

Programs

PARI

a(n) = sum(k=0, n, k*(n+4)^(k-1)*4^(n-k)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} k * (n+4)^(k-1) * 4^(n-k) * |Stirling1(n,k)|.

a(n) = n! * [x^n] ( -log(1 - 4*x)/(4 * (1 - 4*x)^(n/4+1)) ).