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A303271 Number of ordered rooted trees with n non-root nodes such that the maximal outdegree equals three.

%I A303271 #5 Apr 20 2018 12:38:47
%S A303271 1,4,15,53,182,616,2070,6930,23166,77429,258973,867230,2908633,
%T A303271 9772556,32896088,110949072,374934201,1269505482,4306750577,
%U A303271 14638006449,49843505965,170021694271,580954640775,1988357053020,6816047416230,23400699072231,80455436055699
%N A303271 Number of ordered rooted trees with n non-root nodes such that the maximal outdegree equals three.
%H A303271 Alois P. Heinz, <a href="/A303271/b303271.txt">Table of n, a(n) for n = 3..1802</a>
%F A303271 a(n) = A036765(n) - A001006(n).
%p A303271 b:= proc(u, o, k) option remember; `if`(u+o=0, 1,
%p A303271       add(b(u-j, o+j-1, k), j=1..min(1, u))+
%p A303271       add(b(u+j-1, o-j, k), j=1..min(k, o)))
%p A303271     end:
%p A303271 a:= n-> b(0, n, 3)-b(0, n, 2):
%p A303271 seq(a(n), n=3..35);
%Y A303271 Column k=3 of A203717.
%Y A303271 Cf. A001006, A036765.
%K A303271 nonn
%O A303271 3,2
%A A303271 _Alois P. Heinz_, Apr 20 2018