Problem of the Week 820

Pascal's Determinant

Suppose that Pascal's triangle is written as follows:

	1    1    1    1    1  . . .
	1    2    3    4    5  . . .
	1    3    6   10   15  . . .
	1    4   10   20   35  . . .
	1    5   15   35   70  . . .
	.    .    .    .    .
	.    .    .    .    .
	.    .    .    .    .

The first row and column consist entirely of 1s, and every other number is the sum of the number to its left and the number above. For each positive number n, let D_n denote the determinant of the matrix consisting of the first n rows and first n columns of this array. Compute D_n.

© Copyright 1996 Stan Wagon. Reproduced with permission.