Search: id:A076540
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%I A076540
%S A076540 1,3,11,41,154,582,2211,8437,32318,124202,478686,1849498,7161556,
%T A076540 27784460,107980515,420300045,1638238710,6393535170,24980504010,
%U A076540 97704407790,382509199020,1498824792660,5877754713870,23067328421826
%N A076540 Number of branches in all ordered trees with n edges.
%C A076540 Binomial[2n-1,n-2]+binomial[2n-2,n-1]. - David Callan (callan(AT)stat.wisc.edu), 
               Nov 06 2003
%C A076540 Row sums of triangle A136535 - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jan 04 2008
%D A076540 J. Riordan, J. Combinat. Theory, Ser A, 19, 214-222, 1975.
%F A076540 a(n)=(3n^2-2n+1)binom(2n, n)/[2(n+1)(2n-1)]; g.f.=(1-z)(C-1)/sqrt(1-4z), 
               where C=[1-sqrt(1-4z)]/(2z) is the Catalan function.
%e A076540 a(3)=11 because the five ordered trees with 3 edges have 1+3+2+2+3=11 
               branches altogether.
%Y A076540 First differences of A001791. First differences are in A073663.
%Y A076540 Cf. A136535.
%Y A076540 Sequence in context: A001835 A079935 A113437 this_sequence A129637 A084077 
               A027103
%Y A076540 Adjacent sequences: A076537 A076538 A076539 this_sequence A076541 A076542 
               A076543
%K A076540 nonn
%O A076540 1,2
%A A076540 Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 18 2002

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