0,2

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

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).

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

E.g.f.: exp ( (e^(2x) - 3)/2 + e^x ).

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]

Cf. A085483.

u[n,j] is A162663.

Sequence in context: A009132 A125275 A007446 this_sequence A105216 A005977 A059037

Adjacent sequences: A002869 A002870 A002871 this_sequence A002873 A002874 A002875

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jul 09 2009