Search: id:A001004
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%I A001004 M0898 N0339
%S A001004 1,1,2,3,9,20,75,262,1117,4783,21971,102249,489077,2370142,11654465,
%T A001004 57916324,290693391,1471341341,7504177738,38532692207,199076194985,
%U A001004 1034236705992,5400337050086,28329240333758,149244907249629
%N A001004 Number of symmetric dissections of a polygon.
%C A001004 Also number of 2-connected outerplanar graphs on n unlabeled nodes. - 
               S. R. Finch (Steven.Finch(AT)inria.fr), Dec 09 2004
%D A001004 Guanzhang Hu, Group theory method for enumeration of outerplanar graphs, 
               Acta Math. Appl. Sinica 14 (1998) 381-387.
%D A001004 P. Lisonek, Closed forms for the number of polygon dissections. Journal 
               of Symbolic Computation 20 (1995), 595-601.
%D A001004 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.
%D A001004 R. C. Read, On general dissections of a polygon, Aequat. Math. 18 (1978), 
               370-388.
%D A001004 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001004 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001004 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Planar graph growth 
               constants</a>.
%t A001004 f[x_, n_]:=x+Sum[(1/r)*Binomial[s-2, r-1]*Binomial[r+s-1, s]*x^s, {r, 
               1, n}, {s, 2, n}]; F[x_, n_]:=Series[((3x^2-2*x*f[x, n]+f[x, n]^2)- 
               (2+2*x+7*x^2-4*x*f[x, n]+2*f[x, n]^2)*f[x^2, n]+ 2*f[x^2, n]^2)/(4*(2*f[x^2, 
               n]-1))+Sum[If[Mod[k, d]==0, EulerPhi[d]*f[x^d, n]^(k/d)/k, 0], {k, 
               3, n}, {d, 1, k}]/2, {x, 0, n}]; F[x, 22] (Finch)
%Y A001004 Sequence in context: A097075 A036673 A111189 this_sequence A015951 A101531 
               A099607
%Y A001004 Adjacent sequences: A001001 A001002 A001003 this_sequence A001005 A001006 
               A001007
%K A001004 nonn,nice,easy
%O A001004 0,3
%A A001004 N. J. A. Sloane (njas(AT)research.att.com).
%E A001004 More terms from Esa Peuha (esa.peuha(AT)helsinki.fi), Oct 21 2005

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