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A002872
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Number of partitions of 2n objects invariant under a permutation consisting of n 2-cycles.
(Formerly M1786 N0705)
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20
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
Column 2 of A162663. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jul 09 2009
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| E.g.f.: exp ( (e^(2x) - 3)/2 + e^x ).
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MATHEMATICA
| u[0, j_]:=1; u[k_, j_]:=u[k, j]=Sum[Binomial[k-1, i-1]Plus@@(u[k-i, j]#^(i-1)&/@Divisors[j]), {i, k}]; Table[u[n, 2], {n, 0, 12}] [From Wouter Meeussen (wouter.meeussen(AT)pandora.be), Dec 06 2008]
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CROSSREFS
| Cf. A085483.
u[n,j] is A162663.
Sequence in context: A009132 A125275 A007446 * A105216 A193657 A005977
Adjacent sequences: A002869 A002870 A002871 * A002873 A002874 A002875
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jul 09 2009
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