Summary: We consider several nested sums, and show how binomial coefficients, Stirling numbers of the second kind and Gaussian binomial coefficients can be written as nested sums. We use this to find the rate of growth for diagonals of Stirling numbers of the second kind, as well as another proof of a known identity for Gaussian binomial coefficients.

05A10, 11B73, 11B65

nested sums, Stirling numbers, q-nomial coefficients