Séminaire Lotharingien de Combinatoire, B05c (1981), 25 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1982, 182/S-04, p. 59-78.]

Dominique Dumont

Matrices d'Euler-Seidel

Abstract. This paper is a collection of finite-difference calculus tables. What is meant by Euler-Seidel matrix is what our predecessors such as Leibniz, Euler or Seidel constructed when starting with a sequence of numbers they considered the sequence of differences between consecutive terms and iterated the procedure.

First, the two theorems by Euler and Seidel are stated and further applied to various examples. The most striking examples are those in which the Euler-Seidel matrix provides a rapid calculation of the initial sequence of integers that have themselves a combinatorial interpretation. For each example we give the sequence of the first values according to a principle dear to the enumerating practitioners.

Département de mathématique, Université Louis Pasteur, Strasbourg

The following versions are available: