%I A000242 M2798 N1126
%S A000242 1,3,9,25,69,186,503,1353,3651,9865,26748,72729,198447,543159,1491402,
%T A000242 4107152,11342826,31408719,87189987,242603970,676524372,1890436117,
%U A000242 5292722721,14845095153,41708679697,117372283086,330795842217
%N A000242 3rd power of rooted tree enumerator; number of linear forests of 3 rooted 
               trees.
%D A000242 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000242 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000242 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               150.
%H A000242 T. D. Noe, <a href="b000242.txt">Table of n, a(n) for n=3..200</a>
%H A000242 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A000242 G.f.: B(x)^3 where B(x) is g.f. of A000081.
%p A000242 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, x=0, n+1), x,n): seq 
               (a(n), n=3..29); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Aug 21 2008]
%Y A000242 Cf. A000081, A000106, A000300, A000343, A000395.
%Y A000242 Sequence in context: A085327 A069403 A094292 this_sequence A077846 A005322 
               A103780
%Y A000242 Adjacent sequences: A000239 A000240 A000241 this_sequence A000243 A000244 
               A000245
%K A000242 nonn,easy,nice
%O A000242 3,2
%A A000242 N. J. A. Sloane (njas(AT)research.att.com).
%E A000242 More terms from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.