Independent Segregation of Chromosomes

Problem

Consider a collection of coin flips. One of the most natural questions we can ask is if we flip a coin 92 times, what is the probability of obtaining 51 "heads", vs. 27 "heads", vs. 92 "heads"?

Each coin flip can be modeled by a uniform random variable in which each of the two outcomes ("heads" and "tails") has probability equal to 1/2. We may assume that these random variables are independent (see “Independent Alleles”); in layman's terms, the outcomes of the two coin flips do not influence each other.

A binomial random variable X takes a value of k if n consecutive "coin flips" result in k total "heads" and n−k total "tails." We write that X∈Bin(n,1/2).

Given: A positive integer n≤50.

Return: An array A of length 2n in which A[k] represents the common logarithm of the probability that two diploid siblings share at least k of their 2n chromosomes (we do not consider recombination for now).