A117505 - OEIS

%I #8 Aug 30 2019 04:09:24

%S 1,2,1,2,4,3,2,4,16,13,2,4,16,80,67,2,4,16,80,448,381,2,4,16,80,448,

%T 2688,2307,2,4,16,80,448,2688,16896,14589,2,4,16,80,448,2688,16896,

%U 109824,95235,2,4,16,80,448,2688

%N Triangle of coefficients for polynomials used for the column g.f.s of triangle A116880, called CM(1,2).

%C The g.f. G(m,x) for column m=1,2,... of triangle A116880=CM(1,2) is x*(-sum(a(m,k)*x^(k-1),k=1..m) + sum(a(m,k)*x^k,k=0..m)*2*c(2*x))/(1+x), with the o.g.f. c(x) of A000108 (Catalan numbers).

%H W. Lang: <a href="/A117505/a117505.txt">First 10 rows.</a>

%F a(m,m)= A064062(m) =:C(2;m), m>=0 and a(m,k)=2*A052701(k) = C(k)*2^(k+1), for k=1,...,m-1 and C(k):=A000108(k) (Catalan).

%e m=3: G(3,x)= x*(-(4+16*x+13*x^2) +

%e (2+4*x+16*x^2+13*x^3)*2*c(2*x))/(1+x).

%K nonn,easy,tabl

%O 0,2

%A _Wolfdieter Lang_, Apr 13 2006