Search: id:A000243
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%I A000243 M2803 N1128
%S A000243 1,3,9,26,75,214,612,1747,4995,14294,40967,117560,337830,972027,
%T A000243 2800210,8075889,23315775,67380458,194901273,564239262,1634763697,
%U A000243 4739866803,13752309730,39926751310,115988095896,337138003197
%N A000243 Number of trees with n nodes, 2 of which are labeled.
%D A000243 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000243 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000243 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               138.
%H A000243 T. D. Noe, <a href="b000243.txt">Table of n, a(n) for n=2..200</a>
%H A000243 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A000243 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A000243 a(n) = A000107(n)-A000081(n).
%F A000243 G.f.: A(x) = B(x)^2/(1-B(x)), where B(x) is g.f. for rooted trees with 
               n nodes, cf. A000081. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 
               19 2001
%p A000243 b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), 
               k=1..n-1)/(n-1) fi end: s:= proc(n,k) option remember; add(b(n+1-j*k), 
               j=1..iquo(n,k)) end: B:= proc(n) option remember; add (b(k)*x^k, 
               k=1..n) end: a:= n-> coeff (series (B(n-1)^2/(1-B(n-1)), x=0, n+1), 
               x,n): seq (a(n), n=2..27); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 21 2008]
%Y A000243 Cf. A000055, A000081, A000269, A000485, A000526, A000107, A000524, A000444, 
               A000525.
%Y A000243 Sequence in context: A127911 A116423 A077845 this_sequence A076264 A123941 
               A018919
%Y A000243 Adjacent sequences: A000240 A000241 A000242 this_sequence A000244 A000245 
               A000246
%K A000243 nonn,easy,nice
%O A000243 2,2
%A A000243 N. J. A. Sloane (njas(AT)research.att.com).
%E A000243 More terms, new description and formula from Christian G. Bower (bowerc(AT)usa.net), 
               Nov 15 1999.

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