Geodesic
A note on nested sums
Journal of integer sequences, Tome 13 (2010) no. 4
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.
Classification : 05A10, 11B73, 11B65
Keywords: nested sums, Stirling numbers, q-nomial coefficients 
@article{JIS_2010__13_4_a3,
     author = {Butler,  Steve and Karasik,  Pavel},
     title = {A note on nested sums},
     journal = {Journal of integer sequences},
     year = {2010},
     volume = {13},
     number = {4},
     zbl = {1197.05003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_4_a3/}
}
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Butler,  Steve; Karasik,  Pavel. A note on nested sums. Journal of integer sequences, Tome 13 (2010) no. 4. http://geodesic.mathdoc.fr/item/JIS_2010__13_4_a3/