A089500 Denominators for computation of column sequences of triangle A071951 (Legendre-Stirling).

1, 2, 10, 630, 2520, 277200, 97297200, 3405402000, 463134672000, 475176173472000, 16631166071520000, 4207685016094560000, 3786916514485104000000, 98459829376612704000000

Offset: 1

Author

Wolfdieter Lang, Nov 07 2003

Keywords

• nonn

Comments

The k-th column sequence A071951(n+k,k), n>=0, is sum(A089278(k,p)*(p*(p+1))^n,p=1..k)/a(k), k>=1.

Formula

a(n)= N(n)/D(n) with N(n) := sfac(n-1)*sfac(2*n+1)/sfac(n+1)= A089501(n) and D(n) := gcd([seq((2*m+1)*((m*(m+1))^n)*N(n)/((n+m+1)!*(n-m)!), m=1..n)]), where sfac(n)=A000178(n) (superfactorials) and gcd(L) is the greatest common divisor >1 of a list of numbers L.