A125080 Triangle, read by rows, defined by T(n,k) = A000108(n-k)*A001147(k)*C(n,2*k), for k=0..[n/2], n>=0, where A000108 is the Catalan numbers and A001147 is the double factorials.

1, 1, 2, 1, 5, 6, 14, 30, 6, 42, 140, 75, 132, 630, 630, 75, 429, 2772, 4410, 1470, 1430, 12012, 27720, 17640, 1470, 4862, 51480, 162162, 166320, 39690, 16796, 218790, 900900, 1351350, 623700, 39690, 58786, 923780, 4813380, 9909900, 7432425

Offset: 0

Author

Paul D. Hanna, Nov 19 2006

Keywords

• nonn
• tabf

Examples

			Table begins:
1;
1;
2, 1;
5, 6;
14, 30, 6;
42, 140, 75;
132, 630, 630, 75;
429, 2772, 4410, 1470;
1430, 12012, 27720, 17640, 1470;
4862, 51480, 162162, 166320, 39690;
16796, 218790, 900900, 1351350, 623700, 39690; ...
		

Crossrefs

Cf. A115081 (row sums), A115080; A000108, A001147.

Programs

PARI

T(n,k)=binomial(2*n-2*k,n-k)/(n-k+1)*binomial(2*k,k)*k!/2^k*binomial(n,2*k)

PARI

T(n,k)=(2*n-2*k)!*n!/k!/(n-k)!/(n-k+1)!/(n-2*k)!/2^k

Formula

Row sums equals A115081, which is column 0 of triangle A115080.