login
A131635
Triangle T(n,m)=m*n*binomial(m+n,m)^2/(2*(m+n)) read by rows.
1
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
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
KEYWORD
easy,nonn,tabl
AUTHOR
R. J. Mathar, Sep 05 2007
STATUS
approved