%I A001005 M1353 N0520
%S A001005 1,0,1,1,2,5,8,21,42,96,222,495,1177,2717,6435,15288,36374,87516,
%T A001005 210494,509694,1237736,3014882,7370860,18059899,44379535,109298070,
%U A001005 269766655,667224480,1653266565,4103910930,10203669285,25408828065
%N A001005 Number of ways of partitioning n points on a circle into subsets only 
               of sizes 2 and 3.
%D A001005 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001005 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001005 T. S. Motzkin, Relations between hypersurface cross ratios and a combinatorial 
               formula for partitions of a polygon, for permanent preponderance 
               and for non-associative products, Bull. Amer. Math. Soc., 54 (1948), 
               352-360.
%H A001005 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=396">
               Encyclopedia of Combinatorial Structures 396</a>
%H A001005 L. Smiley, <a href="http://www.math.uaa.alaska.edu/~smiley/A001005_7_8.pdf">
               a(7) and a(8)</a>
%H A001005 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A001005 G.f. for a(n+1) satisfies A(x)=x*(1+A(x)^2+A(x)^3). (Bower)
%F A001005 a(n)=sum(((n)!/(k!*j!*(n-k-j+1)!)*[2*k+3*j=n], k=0..floor(n/2), j=0..floor(n/
               3)). - Len Smiley (smiley(AT)mazzy.math.uaa.alaska.edu), Jun 18 2005
%e A001005 a(7)=21: 7 rotations of [12][34][567], 7 rotations of [12][45][367], 
               7 rotations of [12][37][456]
%p A001005 a:=proc(n::nonnegint) local k,j; a(n):=0; for k from 0 to floor(n/2) 
               do for j from 0 to floor(n/3) do if (2*k+3*j=n) then a(n):=a(n)+(n)!/
               (k!*j!*(n-k-j+1)!) fi od od; print(a(n)) end proc; seq(a(i),i=0..30); 
               (Smiley)
%Y A001005 Sequence in context: A087077 A117647 A121568 this_sequence A009735 A137095 
               A092097
%Y A001005 Adjacent sequences: A001002 A001003 A001004 this_sequence A001006 A001007 
               A001008
%K A001005 nonn,eigen
%O A001005 0,5
%A A001005 N. J. A. Sloane (njas(AT)research.att.com).
%E A001005 More terms, formula and comment from Christian G. Bower (bowerc(AT)usa.net), 
               Dec 15 1999.
%E A001005 Additional comments from Len Smiley (smiley(AT)mazzy.math.uaa.alaska.edu), 
               Jun 18 2005