%I A002874 M1863 N0738
%S A002874 1,2,8,42,268,1994,16852,158778,1644732,18532810,225256740,
%T A002874 2933174842,40687193548,598352302474,9290859275060,151779798262202,
%U A002874 2600663778494172,46609915810749130,871645673599372868
%N A002874 Sorting numbers.
%D A002874 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002874 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002874 T. S. Motzkin, Sorting numbers ...: for a link to this paper see A000262.
%D A002874 T. S. Motzkin, Sorting numbers for cylinders and other classification 
               numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, 
               pp. 167-176.
%H A002874 T. D. Noe, <a href="b002874.txt">Table of n, a(n) for n=0..100</a>
%H A002874 <a href="Sindx_So.html#sorting">Index entries for sequences related to 
               sorting</a>
%F A002874 E.g.f.: exp (( exp(3*x) - 4) / 3 + exp(x) ).
%t A002874 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,3],{n,0,12}] [From Wouter Meeussen 
               (wouter.meeussen(AT)pandora.be), Dec 06 2008]
%Y A002874 u[n,j] generates for j=1, A000110 Bell numbers; j=2, A002872 "Sorting 
               numbers"; j=3, A002874 "Sorting numbers"; j=4, A141003 (Mathar); 
               j=5, A036075 "Sorting numbers"; j=6, A141004 (Mathar); j=7, A036077 
               "Sorting numbers" [From Wouter Meeussen (wouter.meeussen(AT)pandora.be), 
               Dec 06 2008]
%Y A002874 Sequence in context: A054993 A005315 A121635 this_sequence A078592 A052646 
               A002856
%Y A002874 Adjacent sequences: A002871 A002872 A002873 this_sequence A002875 A002876 
               A002877
%K A002874 nonn,easy,nice
%O A002874 0,2
%A A002874 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)