## The p-adic Valuation of Eulerian Numbers: Trees and Bernoulli Numbers

- Francis N. Castro, Oscar E. González, Luis A. Medina
- Experimental Mathematics
- 2015

with the initial conditions S(0, 0) = 1 and S(n, 0) = 0 for n > 0. Divisibility properties of integer sequences are expressed in terms of p-adic valuations: given a prime p and a positive integer b, there exist unique integers a, n, with a not divisible by p and n ≥ 0, such that b = ap. The number n is called the p− adic valuation of b. We write n = νp(b… (More)