Search: id:A007852
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%I A007852
%S A007852 1,2,7,29,131,625,3099,15818,82595,439259,2371632,12967707,
%T A007852 71669167,399751019,2247488837,12723799989,72474333715,
%U A007852 415046380767,2388355096446,13803034008095
%N A007852 Antichains in rooted plane trees on n nodes.
%C A007852 Setting both offset to zero, this is the Catalan transform of A007317. 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 29 2009]
%D A007852 M. Klazar, Twelve countings with rooted plane trees, European Journal 
               of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740.
%D A007852 F. Ruskey, "Listing and Counting Subtrees of a Tree", SIAM J. Computing, 
               10 (1981) 141-150.
%H A007852 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A007852 <a href="Sindx_Res.html#revert">Index entries for reversions of series</
               a>
%F A007852 G.f.: A(z) = (1-B(z)-sqrt(1-5z-B(z)))/2, where B(z) = (1-sqrt(1-4z))/
               2.
%F A007852 a[ 1 ] = 1 and for n > 1 a[ n ] = sum( (a[ j ]+b[ j ])*a[ n-j ], j=1..n-1 
               ), where b[ n ] = C(2n-2, n-1)/n (Catalan number).
%F A007852 Also REVERT[A(x)] = x + 2*x^2 + x^3*(A007440(x) (Reversion of Fibonacci) 
               - Olivier Gerard (olivier.gerard(AT)gmail.com), Jul 05 2001
%F A007852 a(n+1)=Sum_{k, 0<=k<=n}A039599(n,k)*A000108(k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Mar 12 2007
%Y A007852 Cf. A007440.
%Y A007852 Sequence in context: A054321 A150664 A132262 this_sequence A110576 A074600 
               A064641
%Y A007852 Adjacent sequences: A007849 A007850 A007851 this_sequence A007853 A007854 
               A007855
%K A007852 nonn
%O A007852 1,2
%A A007852 Martin Klazar (klazar(AT)kam.mff.cuni.cz)
%E A007852 More terms and formulae from fruskey(AT)cs.uvic.ca (Frank Ruskey), 11/
               97.

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