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 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 (list; table; graph; refs; listen; history; text; internal format)
 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: A161687 A245498 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

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Last modified January 28 00:32 EST 2020. Contains 331313 sequences. (Running on oeis4.)