We study the asymptotic growth of sums over the N by N power multiplicationtable defined by i to the power k times j to the power k. Comparing the totalrow-wise sum with the sum along anti-diagonals reveals that their limiting ratiosimplifies to a product involving a Beta function. For integer and half-integer exponents, the Gamma duplication formula produces an exact duality linking theseratios to integer multiples of pi. This framework naturally introduces central binomial coefficients and Catalan numbers, thereby connecting elementary matrixgeometry to the classical Wallis product for pi.
Gokul P (Sat,) studied this question.