Extending Pascal's triangle

AbstractAn alternative is given to Hilton and Pedersen's method of defining binomial coefficients (rn) for any integers n,r. It involves using the usual factorial formula for (rn) via the defining of the factorial ratio n!/r! for any integers n,r. In the process, defining 00 = 1 turns out to have several useful applications. An attempt to extend the binomial theorem to negative exponents suggests viewing the extended Pascal's triangle as binomial coefficients modulo an infinite number