Eigen values of a Toeplitz Matrix

Hello. I have a problem finding the eig(T), my matrix have very very small numbers, my code is:

K=[];
M= [];
for i=0:512
    M =[M,((-1)^(i))*combinatorio(3/4,i)]; %combinatorio is a function that i created to compute nchoosek(a,b) in real numbers
end  

for i=0:512
    if i==0
        K=[K,((-1)^(i))*combinatorio(3/4,0)];
    end
    if i==1
        K=[K,33];
    end    
    if i >1
        K =   [K,0];
        end
end     
T=toeplitz (M,K);
E=eig(T)

When I do this for 512, it generates an error

    Error using eig
    Input matrix contains NaN or Inf.

I think that is becouse the values of the matrix are so small that MatLab thinks they are 0's. and have problems in eig(T), if you have an idea to solve this please help me with this. Thanks.

EDIT:

function [y1] = combinatorio(a,b)
c=a;
if b==0
    y1=1;
end
if b~=0
for i=1:(b-1)
    a=a*(c-i);
end
 y1 = (a/factorial(b));
end

[Walter Roberson]

It would help ifwe had your routine combinatorio

[Juan Rodriguez]

I edit it with that code.

Answer 1

[Walter Roberson]

Your combinatorio finds (-1)^b*gamma(b-a)/gamma(-a) and then finds b! and divides the 2. But at b = 171, b! overflows representable doubles, resulting in inf.

You should reformulate so that in the loop you multiply a by (c-i)/(b+D) where D is -1, 0, or +1, depending on what you need for the factorial logic to work out.