A384171 a(n) = 2^n * n! * binomial(5*n/2,n) * Sum_{k=1..n} 1/(3*n+2*k).

1, 18, 503, 19312, 946009, 56419200, 3967700295, 321506211840, 29497821190065, 3022798062551040, 342204383046633975, 42414460290839347200, 5712600791700063700425, 830773593435129407078400, 129744737403826992957167175, 21657021896289762215460864000, 3847769544999445159548440534625

Offset: 1

Author

Seiichi Manyama, May 21 2025

Keywords

• nonn

Crossrefs

Cf. A384137, A384172.

Programs

PARI

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

Formula

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

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