A076126 Triangle T(n,k) of associated Lah numbers, n>=2, k=1..floor(n/2).

2, 6, 24, 12, 120, 120, 720, 1080, 120, 5040, 10080, 2520, 40320, 100800, 40320, 1680, 362880, 1088640, 604800, 60480, 3628800, 12700800, 9072000, 1512000, 30240, 39916800, 159667200, 139708800, 33264000, 1663200, 479001600

Offset: 2

Author

Vladeta Jovovic, Vladimir Baltic, Oct 31 2002

Keywords

• nonn
• tabf

Comments

Number of partitions of {1,..,n} into k lists of size >1, where a list means an ordered subset, cf. A008297.

Examples

			2; 6; 24, 12; 120,120; 720,1080,120; 5040,10080, 2520; ...
		

Crossrefs

Row sums give A052845, A008306, A008299.

Formula

T(n, k) = n!/k!*binomial(n-k-1, k-1), n>=2, k=1..floor(n/2). G.f.: G.f.: Sum_{n>=2, k=1..floor(n/2)} T(n, k)*x^n*y^k/n! = exp(x^2*y/(1-x))-1.