A116872 Subtriangle of generalized Catalan triangle CM(1,2) = A116880.

1, 3, 7, 13, 29, 41, 67, 147, 195, 247, 381, 829, 1069, 1277, 1545, 2307, 4995, 6339, 7379, 8451, 9975, 14589, 31485, 39549, 45373, 50733, 56829, 66057, 95235, 205059, 255747, 290691, 320707, 351187, 388099

Offset: 1

Author

Wolfdieter Lang, Mar 24 2006

Keywords

• nonn
• easy
• tabl

Comments

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.

Links

• W. Lang: First 10 rows.

Crossrefs

Row sums give A116879.

Formula

a(n,m)=A116880(n,m-1), n>=m>=1.

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.