A131635 Triangle T(n,m)=m*n*binomial(m+n,m)^2/(2*(m+n)) read by rows.

1, 3, 18, 6, 60, 300, 10, 150, 1050, 4900, 15, 315, 2940, 17640, 79380, 21, 588, 7056, 52920, 291060, 1280664, 28, 1008, 15120, 138600, 914760, 4756752, 20612592, 36, 1620, 29700, 326700, 2548260, 15459444, 77297220, 331273800, 45, 2475, 54450

Offset: 1

Author

R. J. Mathar, Sep 05 2007

Keywords

• easy
• nonn
• tabl

Comments

First two columns are essentially A000217 and A006011.

Examples

			Triangle is symmetric in the two indices and starts
1,
3, 18,
6, 60, 300,
10, 150, 1050, 4900,
15, 315, 2940, 17640, 79380,
21, 588, 7056, 52920, 291060, 1280664,
		

Links

• V. J. W. Guo and J. Zeng, A note on two identities arising from enumeration of convex polyominoes, J. Comp. Appl. Math. 180 (2005) pp 413-423.

Programs

Maple

a := proc(n,m) m*n*(binomial(m+n,n))^2/2/(m+n) ; end: for n from 1 to 10 do for m from 1 to n do printf("%d, ",a(n,m)) ; od: od:

Mathematica

Flatten[Table[m*n*Binomial[m+n,m]^2/(2(m+n)),{n,10},{m,n}]] (* Harvey P. Dale, Dec 24 2011 *)

PARI

A131635(n,m) = m*n*binomial(m+n,m)^2/(2*(m+n))

Formula

T(n,m)=m*n*A000290(A007318(n+m,m))/[2(m+n)].