%I A072638
%S A072638 0,1,3,10,66,2278,2598060,3374961778891,5695183504492614029263278,
%T A072638 16217557574922386301420536972254869595782763547560,
%U A072638 131504586847961235687181874578063117114329409897615188504091716162522225834932122128288032336298141
%N A072638 Number of unary-binary rooted trees of height at most n.
%C A072638 A unary-binary tree is one in which the degree of every node is <= 3.
%C A072638 a(n+1) = (a(n)+1) th triangular numbers = A000217(a(n)+1). a(n+1) = (a(n) 
               + 1) * (a(n) + 2) / 2. a(n+1) = A006894(n+2) - 1. [From Jaroslav 
               Krizek (jaroslav.krizek(AT)atlas.cz), Sep 11 2009]
%H A072638 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A072638 a(n+1)=1+(a(n)*(a(n)+3))/2.
%F A072638 Conjecture: a(n)=A006894(n+1)-1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Apr 23 2007
%F A072638 a(n):=C(a(n-1)+2,2),n>=-1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 08 2007
%p A072638 a[ -1]:=0:a[0]:=1:for n from 1 to 50 do a[n]:=binomial(a[n-1]+2,2) od: 
               seq(a[n], n=-1..9); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 08 2007
%Y A072638 Maximal position in A071673 where the value n occurs.
%Y A072638 Binary width of each term: A072641. Cf. A072639, A072640, A072654.
%Y A072638 Sequence in context: A041014 A009400 A004102 this_sequence A080526 A143083 
               A002499
%Y A072638 Adjacent sequences: A072635 A072636 A072637 this_sequence A072639 A072640 
               A072641
%K A072638 nonn
%O A072638 0,3
%A A072638 Antti Karttunen Jun 02 2002
%E A072638 Edited by Christian G. Bower (bowerc(AT)usa.net), Oct 23 2002