The p-adic valuation of Eulerian numbers: trees and Bernoulli numbers

by Francis N. Castro, Oscar E. Gonzalez, and Luis A. Medina

Experimental Mathematics, 24 (2), 2015, 183-195.
In this work we explore the p-adic valuation of Eulerian numbers. We construct a tree whose nodes contain information about the p-adic valuation of these numbers. Using this tree, and some classical results for Bernoulli numbers, we compute the exact p divisibility for the Eulerian numbers when the first variable lies in a congruence class and p satisfies some regularity properties.

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