A383767 a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)/(1 - k*x).

1, 0, 2, 42, 1152, 40520, 1751850, 90087522, 5376546560, 365487900192, 27886922161650, 2360357986720250, 219495753481590432, 22246783602163580616, 2440974108105319141082, 288270640787372104920450, 36459004369727317927680000, 4916744437454382604092493952, 704282170015570676249171941218

Offset: 0

Author

Seiichi Manyama, May 14 2025

Keywords

• nonn

Crossrefs

Cf. A350366.

Programs

PARI

a(n) = polcoef(prod(k=0, n-1, (1+k*x)/(1-k*x)+x*O(x^n)), n);

Formula

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * Stirling2(k+n-1,n-1) for n > 0.