  The definition of the binomial coefficient in terms of gamma functions also
allows non-integer arguments. For nonnegative integer arguments the gamma
functions reduce to factorials, leading to the well-known Pascal triangle.
Using a symmetry formula for the gamma function, this definition is extended to
negative integer arguments, making the symmetry identity for binomial
coefficients valid for all integer arguments. The agreement of this definition
with some other identities and with the binomial theorem is investigated.
