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A157018
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Triangle T(n,k) read by rows: number of k-lists (ordered k-sets) of disjoint 2-subsets of an n-set, n>1, 0<k<=floor(n/2).
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0
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1, 3, 6, 6, 10, 30, 15, 90, 90, 21, 210, 630, 28, 420, 2520, 2520, 36, 756, 7560, 22680, 45, 1260, 18900, 113400, 113400, 55, 1980, 41580, 415800, 1247400, 66, 2970, 83160, 1247400, 7484400, 7484400, 78, 4290, 154440, 3243240, 32432400, 97297200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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FORMULA
| E.g.f.: y*x^2*exp(x)/(2-y*x^2). T(n,k) = Product_{m=1..floor(n/2)} binomial(n-2*m,2) = n!/(2^k*(n-2*k)!).
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EXAMPLE
| For n = 4 we have 12 lists, 6 1-lists: [{1,2}], [{1,3}], [{1,4}], [{2,3}], [{2,4}], [{3,4}] and 6 2-lists: [{1,2},{3,4}], [{3,4},{1,2}], [{1,3},{2,4}], [{2,4},{1,3}], [{1,4},{2,3}] and [{2,3},{1,4}].
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CROSSREFS
| Cf. A126725(row sums), A129684, A000262, A100861, A000680.
Sequence in context: A002853 A184137 A135610 * A203330 A197442 A113497
Adjacent sequences: A157015 A157016 A157017 * A157019 A157020 A157021
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Allan L. Edmonds and Vladeta Jovovic (vladeta(AT)eunet.yu), Feb 21 2009
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