%I A002955 M1140
%S A002955 1,1,1,2,4,8,17,36,79,175,395,899,2074,4818,11291,26626,63184,150691,
%T A002955 361141,869057,2099386,5088769,12373721,30173307,73771453,180800699,
%U A002955 444101658,1093104961,2695730992,6659914175,16481146479,40849449618
%N A002955 Number of rooted trimmed trees with n nodes.
%C A002955 A rooted trimmed tree is a tree with a forbidden limb of length 2.
%C A002955 A rooted tree with a forbidden limb of length k is a rooted tree where 
               the path from any leaf inward hits a branching node or the root within 
               k steps.
%D A002955 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002955 F. Goebel and R. P. Nederpelt, The number of numerical outcomes of iterated 
               powers, Amer. Math. Monthly, 78 (1971), 1097-1103.
%D A002955 R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the 
               laddered parenthesis. Amer. Math. Monthly 80 (1973), 868-876.
%D A002955 K. L. McAvaney, personal communication.
%D A002955 A. J. Schwenk, Almost all trees are cospectral, pp. 275-307 of F. Harary, 
               editor, New Directions in the Theory of Graphs. Academic Press, NY, 
               1973.
%H A002955 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%H A002955 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A002955 a(n) satisfies a=SHIFT_RIGHT(EULER(a-b)) where b(2)=1, b(k)=0 if k != 
               2.
%p A002955 with (numtheory): a:= proc(n) option remember; local d,j,aa; aa:= n-> 
               a(n)-`if`(n=2,1,0); if n<=1 then n else (add (d*aa(d), d=divisors(n-1)) 
               +add (add (d*aa(d), d=divisors(j)) *a(n-j), j=1..n-2))/ (n-1) fi 
               end: seq (a(n), n=1..32); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Sep 06 2008]
%Y A002955 Cf. A002988-A002992, A052318-A052329.
%Y A002955 Sequence in context: A157904 A002845 A072925 this_sequence A093951 A137255 
               A076892
%Y A002955 Adjacent sequences: A002952 A002953 A002954 this_sequence A002956 A002957 
               A002958
%K A002955 nonn,nice,eigen
%O A002955 1,4
%A A002955 N. J. A. Sloane (njas(AT)research.att.com).
%E A002955 More terms, formula and comments from Christian G. Bower (bowerc(AT)usa.net), 
               Dec 15 1999.