%I A036658
%S A036658 0,0,0,0,1,1,3,6,14,29,68,147,337,757,1734,3953,9113,20988,48645,
%T A036658 112909,263084,614201,1438001,3373253,7930660,18679005,44075988,
%U A036658 104173194,246604137,584620470,1387879434,3299067379,7851736348
%N A036658 Number of n-node rooted unlabeled trees with exactly 3 edges at root 
               and otherwise out-degree <=2.
%H A036658 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A036658 Let G036656(x) = g.f. for A036656. G.f.: x^3*cycle_index(S3, G036656), 
               where cycle_index(Sk, f) means apply the cycle index for the symmetric 
               group S_k to f(x).
%F A036658 E.g. cycle_index(S2, f) = (1/2!)*(f^2+subs(x=x^2, f), cycle_index(S3, 
               f) = (1/3!)*(f^3+3*subs(x=x^2, f)*f+2*subs(x=x^3, f)).
%p A036658 CI2 := proc(f) (1/2)*(f^2+subs(x=x^2,f)); end; CI3 := proc(f) (1/6)*(f^3+3*subs(x=x^2,
               f)*f+2*subs(x=x^3,f)); end;
%p A036658 N := 40: G036658 := series(x^3*CI3(G036656),x,N); A036658 := n->coeff(G036658,
               x,n);
%Y A036658 Sequence in context: A038359 A038360 A084174 this_sequence A077067 A083797 
               A131244
%Y A036658 Adjacent sequences: A036655 A036656 A036657 this_sequence A036659 A036660 
               A036661
%K A036658 nonn,nice,easy
%O A036658 0,7
%A A036658 N. J. A. Sloane (njas(AT)research.att.com).
%E A036658 Corrected May 03 2000 - N. J. A. Sloane (njas(AT)research.att.com).