%I A000444 M4641 N1984
%S A000444 9,64,326,1433,5799,22224,81987,293987,1031298,3555085,12081775,
%T A000444 40576240,134919788,444805274,1455645411,4733022100,15302145060,
%U A000444 49223709597,157629612076,502736717207,1597541346522,5059625685739
%N A000444 Partially labeled rooted trees with n nodes (3 of which are labeled).
%D A000444 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000444 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000444 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               134.
%H A000444 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A000444 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A000444 G.f.: A(x) = B(x)^3*(9-8*B(x)+2*B(x)^2)/(1-B(x))^5, where B(x) is g.f. 
               for rooted trees with n nodes, cf. A000081.
%p A000444 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-2)^3*(9-8*B(n-2)+2*B(n-2)^2)/
               (1-B(n-2))^5, x=0, n+1), x,n): seq (a(n), n=3..24); [From Alois P. 
               Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
%Y A000444 Cf. A000081, A000107, A000243, A000269, A000485, A000524-A000526.
%Y A000444 Cf. A042977.
%Y A000444 Sequence in context: A099761 A092396 A018201 this_sequence A143631 A083328 
               A000846
%Y A000444 Adjacent sequences: A000441 A000442 A000443 this_sequence A000445 A000446 
               A000447
%K A000444 nonn
%O A000444 3,1
%A A000444 N. J. A. Sloane (njas(AT)research.att.com).
%E A000444 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 19 2001