b(n, 2n, p)≈πn(4pq)
where n is the number of heads, 2n is the number of trials, and p is the probability of success.
b(n, 2n, p)=(n2n)pn(1−p)2n−n =n!n!(2n)!pnqn
By Stirling's approximation,
≈2πn nn e−n2π 2n 2n2n e−2n pn qn