A092370 Triangle read by rows: T(n,k)=(1/2)*C(n+k,k)*C(n,n-k).

1, 3, 3, 6, 15, 10, 10, 45, 70, 35, 15, 105, 280, 315, 126, 21, 210, 840, 1575, 1386, 462, 28, 378, 2100, 5775, 8316, 6006, 1716, 36, 630, 4620, 17325, 36036, 42042, 25740, 6435, 45, 990, 9240, 45045, 126126, 210210, 205920, 109395, 24310, 55, 1485, 17160

Offset: 1

Author

Benoit Cloitre, Mar 20 2004

Keywords

• nonn
• tabl

Crossrefs

First column = A000217, second column = A050534, main diagonal = A001700, second diagonal = A033876.

Cf. A063007.

Programs

Mathematica

Table[(Binomial[n+k,k]Binomial[n,n-k])/2,{n,10},{k,n}]//Flatten (* Harvey P. Dale, Dec 29 2021 *)

PARI

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

Extensions

Definition corrected by Harvey P. Dale, Dec 29 2021