Search: id:A005750
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%I A005750 M2855
%S A005750 1,1,3,10,39,160,702,3177,14830,70678,342860,1686486,8393681,42187148,
%T A005750 213828802,1091711076,5609297942,28982708389,150496728594,
%U A005750 784952565145,4110491658233,21602884608167,113907912618599
%N A005750 Number of planted matched trees with n nodes.
%C A005750 When convolved with itself gives A000151.
%C A005750 Number of rooted trees with n nodes and edges not attached to root are 
               2-colored or oriented.
%C A005750 Also number of 2-trees (with 2n+1 cells) rooted at a symmetric end-edge. 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 22 2001
%D A005750 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005750 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6.5.
%D A005750 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 75, Eq. (3.5.3).
%D A005750 R. Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 
               (1991), 93-104.
%H A005750 Alois P. Heinz, <a href="b005750.txt">Table of n, a(n) for n = 1..150</
               a>
%H A005750 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=428">
               Encyclopedia of Combinatorial Structures 428</a>
%H A005750 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%H A005750 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A005750 a(n+1) is Euler transform of A000151.
%F A005750 G.f.: A(x) = x*exp( A(x)^2/x + A(x^2)^2/(2x^2) + A(x^3)^2/(3x^3) +...+ 
               A(x^n)^2/(n*x^n) +...). - Paul D. Hanna (pauldhanna(AT)juno.com)
%e A005750 A(x) = x + x^2 + 3*x^3 + 10*x^4 + 39*x^5 + 160*x^6 + 702*x^7 +...
%p A005750 A:= proc(n) option remember; if n=0 then 0 else unapply (convert (series 
               (x*exp (add ((A(n-1)(x^k))^2/(k*x^k), k=1..2*n)), x=0,2*n), polynom), 
               x) fi end: a:= n-> coeff (series ( A(n)(x), x=0, n+1), x,n): seq 
               (a(n), n=1..23); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 20 2008]
%Y A005750 Cf. A058870, A058866, A054581.
%Y A005750 Sequence in context: A007163 A050385 A123768 this_sequence A151068 A151069 
               A151070
%Y A005750 Adjacent sequences: A005747 A005748 A005749 this_sequence A005751 A005752 
               A005753
%K A005750 nonn
%O A005750 1,3
%A A005750 N. J. A. Sloane (njas(AT)research.att.com).
%E A005750 More terms, formula and comment from Christian G. Bower (bowerc(AT)usa.net), 
               Dec 15 1999.

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