# Non-recursive expressions for even-index Bernoulli numbers: A remarkable sequence of determinants

Research paper by Renaat Van Malderen

Indexed on: 20 May '05Published on: 20 May '05Published in: Mathematics - Number Theory

#### Abstract

Bernoulli numbers are usually expressed in terms of their lower index numbers (recursive). This paper gives explicit formulas for Bernoulli numbers of even index. The formulas contain a remarkable sequence of determinants. The value of these determinants for variable dimension is investigated.