%I A030237
%S A030237 1,1,2,1,3,5,1,4,9,14,1,5,14,28,42,1,6,20,48,90,132,
%T A030237 1,7,27,75,165,297,429,8,35,110,275,572,1001,1430,1,9,44,154,
%U A030237 429,1001,2002,3432,4862
%N A030237 Catalan's triangle with right border removed: 1; 1,2; 1,3,5; ...
%C A030237 This triangle appears in the totally asymmetric exclusion process as 
               Y(alpha=1,beta=1,n,m), written in the Derrida et al. reference as 
               Y_n(m) for alpha=1, beta=1. - Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Jan 13 2006.
%D A030237 B. Derrida, E. Domany and D. Mukamel, An exact solution of a one-dimensional 
               asymmetric exclusion model with open boundaries, J. Stat. Phys. 69, 
               1992, 667-687; eqs. (20), (21), p. 672.
%H A030237 W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A030237.text">
               First 10 rows.</a>
%F A030237 m-th entry in row n is (n+m)!/n!/m! /(n+1) (n-m+1).
%Y A030237 Cf. A009766.
%Y A030237 Row sums give A071724(n)= 3*binomial(2*n, n-1)/(n+2), n>=1.
%Y A030237 The following are all versions of (essentially) the same Catalan triangle: 
               A009766, A030237, A033184, A059365, A099039, A106566, A130020, A047072.
%Y A030237 Diagonals give A000108 A000245 A002057 A000344 A003517 A000588 A003518 
               A003519 A001392, ...
%Y A030237 Sequence in context: A117584 A047997 A049069 this_sequence A118243 A134081 
               A134247
%Y A030237 Adjacent sequences: A030234 A030235 A030236 this_sequence A030238 A030239 
               A030240
%K A030237 nonn,tabl
%O A030237 0,3
%A A030237 Wouter L. J. Meeussen (wouter.meeussen(AT)pandora.be).