Algorithm to compute the deep diagonals of Pascal's Triangle

Question

Given the deep diagonals of Pascal's triangle:

          1
        1   1
      1   2   1
    1   3   3   1
  1   4   6   4    1
1   5   10  10   5   1

1st diagonal: 1 1 1 1 1 ...
2nd diagonal: 1 2 3 4 5 ...
3rd diagonal: 1 3 6 10 15 ...
4th diagonal: 1 4 10 20 35 ...

Is there an algorithm to compute the first k terms from any ith diagonal?

Answer 1

Yes, this is covered in Wikipedia. Here you go:

http://en.wikipedia.org/wiki/Pascal%27s_triangle#Calculating_a_row_or_diagonal_by_itself