A384167 a(n) = 2^n * n! * binomial(3*n/2,n) * Sum_{k=1..n} 1/(n+2*k).

1, 10, 143, 2736, 66009, 1926912, 66086271, 2605455360, 116123049585, 5774107852800, 316921177332495, 19032668386099200, 1241454631056114825, 87402945316493721600, 6606130538582006306175, 533534147838972474163200, 45855293972076668267481825, 4178822478568980876361728000

Offset: 1

Author

Seiichi Manyama, May 21 2025

Keywords

• nonn

Crossrefs

Cf. A098118, A384168, A384169.

Cf. A113551.

Programs

PARI

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

Formula

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

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