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Search: id:A002872
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| A002872 |
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Sorting numbers.
(Formerly M1786 N0705)
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+0
15
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| 1, 2, 7, 31, 164, 999, 6841, 51790, 428131, 3827967, 36738144, 376118747, 4086419601, 46910207114, 566845074703, 7186474088735, 95318816501420, 1319330556537631, 19013488408858761, 284724852032757686
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = number of symmetric partitions of the set {-n,...,-1,1,...,n}. A partition of {-n,...,-1,1,...,n} into nonempty subsets X_1,...,X_k is `symmetric' if for each i, -X_i=X_j for some j. a(n) = S_B(n,1)+...+S_B(n,n) where S_B(n,k) is as in A085483. a(n) is the n-th Bell number of `type B'. - James East (jameseastseq(AT)hotmail.com), Aug 18 2003
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REFERENCES
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T. S. Motzkin, Sorting numbers ...: for a link to this paper see A000262.
T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
J. Quaintance, Letter representations of rectangular m x n x p proper arrays
Index entries for sequences related to sorting
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FORMULA
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E.g.f.: exp ( (e^(2x) - 3)/2 + e^x ).
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CROSSREFS
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Cf. A085483.
Sequence in context: A009132 A125275 A007446 this_sequence A105216 A005977 A059037
Adjacent sequences: A002869 A002870 A002871 this_sequence A002873 A002874 A002875
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
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