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

1,2

Comments

First two columns are essentially A000217 and A006011.

Links

Table of n, a(n) for n=1..39.

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.

Formula

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

Example

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,

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 *)

Prog

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

Crossrefs

Sequence in context: A245498 A350703 A120647 * A324554 A007475 A324889

Adjacent sequences: A131632 A131633 A131634 * A131636 A131637 A131638

Keyword

easy,nonn,tabl

Author

R. J. Mathar, Sep 05 2007

Status

approved