Search: id:A115195
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%I A115195
%S A115195 1,2,3,4,10,13,8,28,54,67,16,72,180,314,381,32,176,536,1164,1926,2307,
%T A115195 64,416,1488,3816,7668,12282,14589,128,960,3936,11568,26904,51468,80646,
%U A115195 95235,256,2176,10048,33184,86992,189928,351220,541690,636925,512,4864
%N A115195 Triangle of numbers, called Y(1,2), related to generalized Catalan numbers 
               A062992(n)=C(2;n+1)=A064062(n+1).
%C A115195 This triangle Y(1,2) appears in the totally asymmetric exclusion process 
               for the (unphysical) values alpha=1, beta=2. See the Derrida et al. 
               refs. given under A064094, where the triangle entries are called 
               Y_{N,K} for given alpha and beta.
%C A115195 The main diagonal (M=1) gives the generalized Catalan sequence C(2,n+1):=A064062(n+1).
%C A115195 The diagonal sequences give A064062(n+1), 2*A084076, 4*A115194, 8*A115202, 
               16*A115203, 32*A115204 for n+1>= M=1,..,6.
%H A115195 W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A115195.text">
               First 10 rows.</a>
%F A115195 G.f. m-th diagonal, m>=1: ((1 + 2*x*c(2*x))*(2*x*c(2*x))^m)/(2*x*(1+x)) 
               with c(x) the o.g.f. of A000108 (Catalan).
%Y A115195 Row sums give A115196.
%Y A115195 Sequence in context: A005456 A100773 A131120 this_sequence A095384 A115899 
               A085934
%Y A115195 Adjacent sequences: A115192 A115193 A115194 this_sequence A115196 A115197 
               A115198
%K A115195 nonn,easy,tabl
%O A115195 0,2
%A A115195 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Feb 23 2006

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