#include<cmath>
#include<list>

...

double prob(int n, int k, double p) {
    std::list<double> buf(n-1,0.0);
    buf.push_back(pow(p,n));

    for(int i=n; i<k; i++) {
        buf.push_back(buf.back()+(1-p)*pow(p,n)*(1-buf.front()));
        buf.pop_front();
    }

    return buf.back();
}