Problem 55980. Generate Pascal's Triangle Matrix

Ben Placek

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Pascal's triangle is an arrangement of numbers where each value is the sum of the values adjacent to it in the previous row:
The values can also be calculated directly. The  value of the  row is . For example, the fifth row is 1, 4, 6, 4, 1:
nchoosek(4,0)
ans =
1
nchoosek(4,1)
ans =
4
nchoosek(4,2)
ans =
6
nchoosek(4,3)
ans =
4
nchoosek(4,4)
ans =
1
Given a positive integer n, return an n-by-n matrix that represents the values of the first n rows of Pascal's triangle. The first k values of the kth row of the matrix will be the values from Pascal's triangle; the remaining n-k values should be 0.
For example, for n = 6, the output should be
1     0     0     0     0     0
1     1     0     0     0     0
1     2     1     0     0     0
1     3     3     1     0     0
1     4     6     4     1     0
1     5    10    10     5     1