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Search: id:A105748
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| A105748 |
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Number of ways to use the elements of {1,..,k}, 0<=k<=2n, once each to form a collection of n (possibly empty) sets, each with at most 2 elements. |
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4
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| 1, 3, 10, 47, 313, 2744, 29751, 383273, 5713110, 96673861, 1830257967, 38326484944, 879473289521, 21944639630923, 591545277653354, 17131028946645255, 530424623323416617
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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R. A. Proctor, Let's Expand Rota's Twelvefold Way for Counting Partitions! arXiv math.CO.0606404.
Index entries for related partition-counting sequences
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FORMULA
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Sum[(k+i)!/i!/(k-i)!/2^i, 0<=i<=k<=n]
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EXAMPLE
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10 = |{ {{},{}}, {{},{1}}, {{},{1,2}}, {{1},{2}}, {{1},{2,3}}, {{2},{1,3}}, {{3},{1,2}}, {{1,2},{3,4}}, {{1,3},{2,4}}, {{1,4},{2,3}} }|
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MATHEMATICA
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Sum[(k+i)!/i!/(k-i)!/2^i, {k, 0, n}, {i, 0, k}]
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CROSSREFS
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First differences: A001515.
Replacing "collection" by "sequence" gives A003011.
Replacing "sets" by "lists" gives A105747.
Sequence in context: A000849 A092429 A005651 this_sequence A140964 A005921 A143921
Adjacent sequences: A105745 A105746 A105747 this_sequence A105749 A105750 A105751
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KEYWORD
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nonn,easy
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AUTHOR
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Robert A. Proctor (www.math.unc.edu/Faculty/rap/), Apr 18 2005
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