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).

(In reply to re: computer assisted solution by Charlie)

There is a way of doing it involving matrix multiplication. https://en.wikipedia.org/wiki/Pascal_matrix

It looks simple but actually the underlying theory is quite complicated.

Posted by broll on 2018-04-12 03:02:17