binomial determinant

[benoit]

Thanks for exploring this further.

> det([binomial(a_i*z_j,j)]
>
> = 1/(C(n))* prod(a_i,i=1..n)*prod(a_i-a_j, 1<=j<i 
> <=n)*prod(z_j^j,j=1..n)
>
> where C(n) = A000178(n) = the Vandermonde determinant of the numbers
> 1,2,..(n+1) (among other things).


And what about  a  "full" generalisation :

det([binomial(a_i*z_j,b_j)] ?  since C(n) is obtained from b_j=j


Benoit.