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A119743
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Triangle read by rows: row n gives number of matchings of size 0<=k<=n (edges) in the complete graph on 2*n >= 2 vertices.
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1
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1, 1, 1, 6, 3, 1, 15, 45, 15, 1, 28, 210, 420, 105, 1, 45, 630, 3150, 4725, 945, 1, 66, 1485, 13860, 51975, 62370, 10395, 1, 91, 3003, 45045, 315315, 945945, 945945, 135135, 1, 120, 5460, 120120, 1351350, 7567560, 18918900, 16216200, 2027025, 1, 153, 9180
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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REFERENCES
| The special case m(n,n) appears in: Flajolet, P. and Noy, M., "Analytic Combinatorics of Chord Diagrams", INRIA Research Report, ISRN INRIA/RR-3914-FR+ENG, March 2000.
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FORMULA
| T(n,k)=(2*n)! / ((2*n-2*k)!*k!*2^k).
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EXAMPLE
| For example, T(3,2) is the number of matchings composed of any two edges of the complete graph on 6 vertices. Then T(3,2) = a(3*(3+1)/2+2) = a(8) = 45. Similarly, T(2,2)=a(5)=3 since the only matchings of size 2 on the K_4 are {{0,1},{2,3}}, {{0,3}{1,2}} and {{0,2},{1,3}}.
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CROSSREFS
| Sequence in context: A195494 A154969 A192741 * A108451 A122178 A126445
Adjacent sequences: A119740 A119741 A119742 * A119744 A119745 A119746
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KEYWORD
| nonn,tabl
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AUTHOR
| Swapnil P. Bhatia (sbhatia(AT)cs.unh.edu), Jul 29 2006
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