Search: id:A000485
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%I A000485 M5008 N2156
%S A000485 16,125,680,3135,13155,51873,195821,715614,2550577,8911942,30640888,
%T A000485 103951415,348724844,1158722880,3818514232,12493703403,40620949971,
%U A000485 131336770375,422536529249,1353341880777,4317248276746,13722302173753
%N A000485 Partially labeled trees with n nodes (4 of which are labeled).
%D A000485 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000485 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000485 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               138.
%H A000485 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A000485 G.f.: A(x) = B(x)^4*(16-19*B(x)+6*B(x)^2)/(1-B(x))^5, where B(x) is g.f. 
               for rooted trees with n nodes, cf. A000081.
%p A000485 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-3)^4*(16-19*B(n-3)+6*B(n-3)^2)/
               (1-B(n-3))^5, x=0, n+1), x,n): seq (a(n), n=4..25); [From Alois P. 
               Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
%Y A000485 Cf. A000055, A000107, A000243, A000269, A000444, A000524-A000526.
%Y A000485 Sequence in context: A125353 A126511 A067442 this_sequence A007787 A067470 
               A133111
%Y A000485 Adjacent sequences: A000482 A000483 A000484 this_sequence A000486 A000487 
               A000488
%K A000485 nonn
%O A000485 4,1
%A A000485 N. J. A. Sloane (njas(AT)research.att.com).
%E A000485 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 19 2001

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