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Search: id:A108410
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| A108410 |
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Triangle T(n,k) read by rows: number of 12312-avoiding matchings on [2n] with exactly k crossings (n >= 1, 0 <= k <= n-1 ). |
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+0
2
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| 1, 2, 1, 5, 5, 2, 14, 21, 15, 5, 42, 84, 84, 49, 14, 132, 330, 420, 336, 168, 42, 429, 1287, 1980, 1980, 1350, 594, 132, 1430, 5005, 9009, 10725, 9075, 5445, 2145, 429, 4862, 19448, 40040, 55055, 55055, 40898, 22022, 7865, 1430, 16796, 75582
(list; table; graph; listen)
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OFFSET
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1,2
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REFERENCES
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W. Y. C. Chen, T. Mansour and S. H. F. Yan, Matchings avoiding partial patterns, The Electronic Journal of Combinatorics 13, 2006, #R112, Theorem 2.2.
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LINKS
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W. Y. C. Chen, T. Mansour and S. H. F. Yan, Matchings avoiding partial patterns
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FORMULA
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T(n, k)=Sum[i=n..2n-1, (-1)^(n+k+i)/i*C(i, n)*C(3n, i+1+n)*C(i-n, k) ].
T(n,k)=C(n-1+k,n-1)C(2n-k,n+1)/n (0<=k<=n-1). [Chen et al.] - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2006
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EXAMPLE
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1
2,1
5,5,2
14,21,15,5
42,84,84,49,14
132,330,420,336,168,42
429,1287,1980,1980,1350,594,132
1430,5005,9009,10725,9075,5445,2145,429
4862,19448,40040,55055,55055,40898,22022,7865,1430
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MAPLE
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T:=(n, k)->binomial(n-1+k, n-1)*binomial(2*n-k, n+1)/n: for n from 1 to 10 do seq(T(n, k), k=0..n-1) od; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 19 2006
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CROSSREFS
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Left-hand columns include A000108 and A002054. Right-hand columns include A000108 and A007851+1. Row sums are A001764.
Sequence in context: A059340 A046757 A118244 this_sequence A058116 A058118 A124226
Adjacent sequences: A108407 A108408 A108409 this_sequence A108411 A108412 A108413
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 03 2005
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