First, Euler gives a few relations on products and sums of binomial coefficients, then a relation on the sums of squares of binomial coefficients. Then he does a bit with the integral for the beta function and finds analogous relations for sums and products of generalized binomial coefficients. This article is notable in part because Euler uses the fairly modern-looking notation [m/n] for binomial coefficients.
Original Source Citation
Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 1781: I, pp. 74-111.
Opera Omnia Citation
Series 1, Volume 15, pp.528-568.