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A131635
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Triangle T(n,m)=m*n*binomial(m+n,m)^2/(2*(m+n)) read by rows.
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1
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| First two columns are essentially A000217 and A006011.
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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.
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FORMULA
| T(n,m)=m*n*A000290(A007318(n+m,m))/[2(m+n)].
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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,
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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:
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MATHEMATICA
| Flatten[Table[m*n*Binomial[m+n, m]^2/(2(m+n)), {n, 10}, {m, n}]] (* From Harvey P. Dale, Dec 24 2011 *)
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PROG
| (PARI) A131635(n, m) = m*n*binomial(m+n, m)^2/(2*(m+n))
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CROSSREFS
| Sequence in context: A082057 A161687 A120647 * A007475 A098874 A077104
Adjacent sequences: A131632 A131633 A131634 * A131636 A131637 A131638
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 05 2007
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