17 01 2010

A BINOMIAL PLAY:

Our contributor Raymond Rogers has sent an alternate proof for:

$\displaystyle det{\bigg[ \binom{i+j+k}{i} \bigg]}_{0\leq i,j \leq n} =\binom{n+k+1}{k+1}$

This expression is identical to the one found in the post Binomial Matrix (III), but here the matrices are indexed from zero instead of one.

The proof is entitled A BINOMIAL DETERMINATE,A VERY SHORT PLAY IN THREE ACTS, and it is based on Vandermonde’s identity.

Thank you Raymond.

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