I've been playing with Q-factorials: QF(0) == 1 QF(N+1) == QF(N) * (1 + Q + Q^2 + ... + Q^N). When Q=1, this gives QF(N) = N!. The degree of QF(N) is Triangle(N-1) = N(N-1)/2. Q-binomials seem to be polynomials: QB(A,B) = QF(A+B) / (QF(A) QF(B)). The degree of QB(A,B) is AB. The degree of QB(A,B,C) = QF(A+B+C) / (QF(A)QF(B)QF(C)) is AB+AC+BC. Etc. Perhaps we can use some of our standard bag of tricks for defining QF(N) for non-integer N. Put QF(Z) ~= Q ^ [ Z(Z-1)/2 ] for RealPart(Z) large, and divide by (Q^Z-1)/(Q-1) to go from Q(Z) to Q(Z-1). There's a set of functional equations similar to X! (X+1/2)! = (2X+1)! * stuff. Presumably there's also a reflection equation with QF(Z) QF(-Z) = more-stuff that looks like pi Z / sin(pi Z). Rich