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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
*a*_{i,j}=*a*_{i-1,j}+*a*_{i,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.

The following versions are available:

**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.