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%I #6 Aug 30 2019 03:38:43
%S 1,3,7,13,29,41,67,147,195,247,381,829,1069,1277,1545,2307,4995,6339,
%T 7379,8451,9975,14589,31485,39549,45373,50733,56829,66057,95235,
%U 205059,255747,290691,320707,351187,388099
%N Subtriangle of generalized Catalan triangle CM(1,2) = A116880.
%C This triangle a(n,m) appears for the unnormalized one-point function T(n,n+m-1) in the totally asymmetric exclusion process (see A067323 for the references) for the (unphysical) values alpha=1, beta=2.
%H W. Lang: <a href="/A116872/a116872.txt">First 10 rows.</a>
%F a(n,m)=A116880(n,m-1), n>=m>=1.
%F G.f. for column m>=1: (x^m)*(-(C2(m) + ((2^2)/x^(m-1))*(c(m-1,2*x)-1)/(2*x)) + 2*(C2(m-1) + (2/x^(m-1))*c(m-2,2*x))*c(2*x))/(1+x) where C2(n):=A064062(n), c(m,x):=sum(C(k)*x^k,k=0..m) with C(k):=A000108(k) (Catalan numbers) and c(x) is the g.f. of A000108.
%Y Row sums give A116879.
%K nonn,easy,tabl
%O 1,2
%A _Wolfdieter Lang_, Mar 24 2006
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