[CLN-list] efficient calculation of binomial

[Silvestre Abruzzo]

I need to initialize a vector with the binomial coefficients. The code 
is like the following:

for(size_t i=1; i<n;i++){
    nl[i]=cln::binomial(m,m-i);
}

where are involved very big number, something like m=10^10 and n=10^6. 
My purpose is to optimize the preceding optimization by using the result 
of the preceding iteration, i.e.

    binomial(n, n-(i+1))=binomial(n, i)* (n-i)/(i+1)

I tried to implement the multiplication  by storing the result of of 
(n-i)/(i+1) in one cl_RA number, but unfortunately the performance are 
worst than the direct calculation. Do you have any idea how to 
initialize efficiently this vector?

Thank you for your help,

Silvestre Abruzzo