Journal of Integer Sequences, Vol. 13 (2010), Article 10.4.4

A Note on Nested Sums

Steve Butler
Department of Mathematics
Los Angeles, CA 90095

Pavel Karasik
Santa Monica College
Santa Monica, CA 90405


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.

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(Concerned with sequences A000217 A001296 A001297 A001298 A027480 A033487 A036969 A111999 A112494.)

Received October 8 2009; revised version received April 5 2010. Published in Journal of Integer Sequences, April 5 2010.

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