Séminaire Lotharingien de Combinatoire, B47g (2002), 19 pp.

Christian Krattenthaler

Evaluations of Some Determinants of Matrices Related to the Pascal Triangle

Abstract. We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence ai,j=ai-1,j+ai,j-1, or variations thereof. These evaluations were either conjectured or extend conjectures by Roland Bacher [J. Théorie Nombres Bordeaux 14 (2002), 19-41].

Received: January 12, 2002; Accepted: February 19, 2002; Final Version: March 25, 2002.

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Comment by the author: It is much easier to prove Theorem 4 by appealing to (the more general) Proposition 1 in the author's paper "Advanced Determinant Calculus," Séminaire Lotharingien Combin. 42 ("The Andrews Festschrift") (1999), Article B42q, 67 pp.