%I A000526 M5387 N2340
%S A000526 125,1296,8716,47787,232154,1040014,4395772,17781210,69498964,
%T A000526 264248924,982218072,3582421612,12857819052,45515994861,159205157535,
%U A000526 551049504784,1889714853263,6427147635062,21698583468717
%N A000526 Partially labeled trees with n nodes (5 of which are labeled).
%D A000526 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000526 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000526 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               138.
%H A000526 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A000526 G.f.: A(x) = B(x)^5*(125-204*B(x)+118*B(x)^2-24*B(x)^3)/(1-B(x))^7, where 
               B(x) is g.f. for rooted trees with n nodes, cf. A000081.
%p A000526 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-4)^5* (125-204*B(n-4) +118*B(n-4)^2 
               -24*B(n-4)^3)/ (1-B(n-4))^7, x=0, n+1),x,n): seq (a(n), n=5..23); 
               [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
%Y A000526 Cf. A000055, A000107, A000243, A000269, A000444, A000485, A000524, A000525.
%Y A000526 Sequence in context: A016815 A088896 A016851 this_sequence A016971 A030082 
               A017043
%Y A000526 Adjacent sequences: A000523 A000524 A000525 this_sequence A000527 A000528 
               A000529
%K A000526 nonn
%O A000526 5,1
%A A000526 N. J. A. Sloane (njas(AT)research.att.com).
%E A000526 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 19 2001