### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Andrew Baxter**, Rutgers University, baxter{at} math [dot] rutgers [dot] edu
**Lara Pudwell**, Rutgers University, lpudwell {at} math [dot] rutgers [dot] edu
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: p-adic pictures from irresistible sequences

Speaker: **Victor Moll**, Tulane University

Date: Thursday, November 29, 2007 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Legendre's formula *ν*_{p}(n!)=*(n-s*_{p}(n))/(p-1) is the simplest instance of the *p*-adic valuation for a sequence defined by a first order recurrence *t*_{n}=*Q(n)t*_{n-1}.
Here *Q* is a polynomial with integer coefficients and *s*_{p}(n) is the sum of the digits of *n* in base *p*.

In this talk we describe the asymptotics of *ν*_{p}(t_{n}) as *n → ∞*

The extension to the case *t*_{n}=*Q*_{1}(n)t_{n-1}+Q_{2}(n)t_{n-2}
will be illustrated with the *p*-adic valuation of the Stirling numbers.

Joint work with T. Amdeberhan, Dante Manna and Luis Medina.