Prime-power factorization of binomial coefficients
Volume 193 / 2020
Acta Arithmetica 193 (2020), 49-74 MSC: Primary 11N37, 11N60, 11N69; Secondary 11B65. DOI: 10.4064/aa180814-10-4 Published online: 13 December 2019
Given a sequence of (highly divisible) positive integers, one may inquire how the powers behave to which various primes appear in the prime-power factorization of the terms of the sequence. Here we deal with this question for several sequences related to factorials, including the sequence of middle binomial coefficients, the sequence of Catalan numbers, and the (double) sequence of all binomial coefficients. We also obtain a similar result for several factorial sequences simultaneously.