Search: id:A002067
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%I A002067 M4458 N1889
%S A002067 1,1,7,127,4369,243649,20036983,2280356863,343141433761,65967241200001,
%T A002067 15773461423793767,4591227123230945407,1598351733247609852849,655782249799531714375489,
%U A002067 313160404864973852338669783,172201668512657346455126457343,108026349476762041127839800617281
%N A002067 a(n) = Sum_{k=0..n-1} binomial(2*n,2*k)*a(k)*a(n-k-1).
%C A002067 Also number of increasing rooted triangular cacti of 2n+1 nodes. (In 
               an increasing rooted graph, nodes are numbered and numbers increase 
               as you move away from root.)
%D A002067 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002067 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002067 Cf. Chapter 5 of F. Bergeron, G. Labelle and P. Leroux, Combinatorial 
               Species and Tree-Like Structures, Camb. 1998.
%H A002067 T. D. Noe, <a href="b002067.txt">Table of n, a(n) for n=0..50</a>
%H A002067 Wikipedia, <a href="http://en.wikipedia.org/wiki/Error_function">Error 
               Function</a>
%H A002067 <a href="Sindx_Ca.html#cacti">Index entries for sequences related to 
               cacti</a>
%F A002067 We have a(n)=b(2n+1), where e.g.f. of b satisfies B'(x)=exp(B(x)^2/2).
%p A002067 a:=proc(n) option remember; if n <= 0 then RETURN(1); else RETURN( add( 
               binomial(2*n,2*k)*a(k)*a(n-k-1), k=0..n-1 ) ); fi; end;
%Y A002067 The sequence of fractions A092676/A132467 is closely related.
%Y A002067 Periods: A122149, A122159.
%Y A002067 Sequence in context: A025166 A139291 A092676 this_sequence A138523 A034670 
               A020516
%Y A002067 Adjacent sequences: A002064 A002065 A002066 this_sequence A002068 A002069 
               A002070
%K A002067 nonn,eigen,easy,nice
%O A002067 0,3
%A A002067 N. J. A. Sloane (njas(AT)research.att.com).
%E A002067 Alternate description, formula and comment from Christian G. Bower (bowerc(AT)usa.net).
%E A002067 New definition and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Oct 22 2005

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