Pascal Triangle/binomial numbers


From the "upper diamond" of Pascal's Triangle ("tilt your head 45 degrees",
if necessary), construct the square matrices:

A_1 = { [1] },

A_2 = { [1, 1], [1, 2] },

A_3 = { [1, 1, 1], [1, 2, 3], [1, 3, 6] },

etc.

I am trying to show that each of these matrices A_n, n = 1, 2, 3, ... are
positive semi-definite. Calculations suggest that they are. I would
appreciate any suggestions or references that may be of help. I am hoping
that if I look at things the right way, that it will be obvious.

Thanks,
Bill


.

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