Geodesic
A counting function generalizing binomial coefficients and some other classes of integers
Journal of integer sequences, Tome 17 (2014) no. 3
We define a counting function that is related to the binomial coefficients. For this function, we derive an explicit expression. In some particular cases, we prove simpler explicit formulae. We also derive a formula for the number of (0,1)-matrices, having a fixed number of 1's, and having no zero rows and zero columns. Further, we show that our function satisfies several recurrence relations.
Classification : 05A10, 11B19
Keywords: binomial coefficient, counting function, delannoy number, figurate number, coordination sequence, lattice path 
@article{JIS_2014__17_3_a3,
     author = {Janji\'c,  Milan and Petkovi\'c,  Boris},
     title = {A counting function generalizing binomial coefficients and some other classes of integers},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {3},
     zbl = {1292.05016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_3_a3/}
}
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%A Petković,  Boris
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Janjić,  Milan; Petković,  Boris. A counting function generalizing binomial coefficients and some other classes of integers. Journal of integer sequences, Tome 17 (2014) no. 3. http://geodesic.mathdoc.fr/item/JIS_2014__17_3_a3/