A384172 a(n) = 4^n * n! * binomial(7*n/4,n) * Sum_{k=1..n} 1/(3*n+4*k).

1, 24, 851, 40832, 2483269, 183241728, 15912395295, 1590131687424, 179766351690345, 22685041361848320, 3161081216499580395, 482101740659382681600, 79876921394710650447405, 14287114673531430042009600, 2743817201103924825303993975, 563131793021994402478188134400

Offset: 1

Author

Seiichi Manyama, May 21 2025

Keywords

• nonn

Crossrefs

Cf. A384137, A384171.

Cf. A384166.

Programs

PARI

a(n) = sum(k=0, n, k*(3*n+4)^(k-1)*4^(n-k)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=0..n} k * (3*n+4)^(k-1) * 4^(n-k) * |Stirling1(n,k)|.

a(n) = n! * [x^n] ( -log(1 - 4*x)/(4 * (1 - 4*x)^(3*n/4+1)) ).