Berke Güleç

Modular Periodicity of the Euler Up/Down Numbers at Odd Prime Powers

Let E_n denote the number of alternating permutations of {1,...,n}, equivalently characterized by Σ_{n≥0} E_n z^n/n! = sec z + tan z. For every q≥1, the sequence (E_n mod q)_{n≥0} is eventually periodic; let d(q) and s(q) denote its minimal eventual period and preperiod. For ever...