three binomial(n,k) definitions

[N. J. A. Sloane]

let me go on record as saying that binomial(n,k) and C(n,k)
are (and always will be) the same in the EIS

- and that their definition is the official one 
given by if(k<0,0,prod(i=0,k-1,n-i)/k!)
and used by every writer on combinatorics (especially Riordan
and Comtet, and possibly even by Euler)

It is unfortunate that Maple's definition is wrong.

NJAS