The function cosh(x) is defined as (exp(x)+exp(-x))/2 and therefore as x increases in size, the value of cosh(x) increases exponentially. I see that your values of Ln(n) are increasing up to approximately 1224 as n reaches nmax. This will make cosh(x) have +inf in the matlab "double" format. Since you are dividing by cosh(x), you will get zeros in Bn(n) for these larger values of n and very small values for many of the other values of n.
In other words, I am saying the behavior you are seeing is inherent in the numbers you are using. There is presumably nothing wrong with matlab's cosh(x) function - it is giving the values it is supposed to give. You can check it by substituting (exp(x)+exp(-x))/2 in place of cosh(x) and seeing if you get the same results.
By the way, you should be looking at your results with "format long", not the default "format short".
