A BINOMIAL PLAY:
Our contributor Raymond Rogers has sent an alternate proof for:
$latex \displaystyle det{\bigg[ \binom{i+j+k}{i} \bigg]}_{0\leq i,j \leq n} =\binom{n+k+1}{k+1}$
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.
Archives:
[a]-120510-Binomial-Play-R.Rogers.pdf
Links:
[1]-Raymond Rogers, Lamm´s Equation, Confluent Hypergeometric Equations- Lamm´s Equation Blogspot
