The Number of Binomial Coefficients Divisible by a Fixed Power of a Prime
There are binomial coefficients for every non-negative integer . Choose a prime number , and split the binomial coefficients into sets according to the highest power of that divides them. This Demonstration uses a combinatorial formula to compute the sizes of these sets. The first set is made up of the binomial coefficients not divisible by .
W.B. Everett, "Number of Binomial Coefficients Divided by a Fixed Power of a Prime," arXiv.org, submitted Oct 8, 2007, http://arxiv.org/abs/0710.1468.