%I A000524 M1927 N0761
%S A000524 2,9,34,119,401,1316,4247,13532,42712,133816,416770,1291731,3987444,
%T A000524 12266845,37627230,115125955,351467506,1070908135,3257389088,
%U A000524 9892759091,30002923380,90879555521,274963755791,831064788976
%N A000524 Number of rooted trees with n nodes, 2 of which are labeled.
%D A000524 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000524 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000524 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               134.
%H A000524 T. D. Noe, <a href="b000524.txt">Table of n, a(n) for n=2..200</a>
%H A000524 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A000524 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A000524 G.f.: A(x) = B(x)^3+2*B(x)^2 where B(x) is g.f. of A000107.
%F A000524 G.f.: A(x) = B(x)^2*(2-B(x))/(1-B(x))^3, where B(x) is g.f. for rooted 
               trees with n nodes, cf. A000081. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Oct 19 2001
%p A000524 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*(2-B(n-1))/(1-B(n-1))^3, 
               x=0, n+1), x,n): seq (a(n), n=2..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 21 2008]
%Y A000524 Cf. A000081, A000107, A000243, A000269, A000444, A000485, A000525, A000526.
%Y A000524 Sequence in context: A150935 A150936 A109719 this_sequence A120989 A010763 
               A077234
%Y A000524 Adjacent sequences: A000521 A000522 A000523 this_sequence A000525 A000526 
               A000527
%K A000524 nonn,easy,nice
%O A000524 2,1
%A A000524 N. J. A. Sloane (njas(AT)research.att.com).
%E A000524 More terms, new description and formula from Christian G. Bower (bowerc(AT)usa.net), 
               Nov 15 1999.