Geodesic
A counting function generalizing binomial coefficients and some other classes of integers
Journal of integer sequences, Tome 17 (2014) no. 3.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_3_a3/}
}
TY  - JOUR
AU  - Janjić, Milan
AU  - Petković, Boris
TI  - A counting function generalizing binomial coefficients and some other classes of integers
JO  - Journal of integer sequences
PY  - 2014
VL  - 17
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2014__17_3_a3/
LA  - en
ID  - JIS_2014__17_3_a3
ER  - 
%0 Journal Article
%A Janjić, Milan
%A Petković, Boris
%T A counting function generalizing binomial coefficients and some other classes of integers
%J Journal of integer sequences
%D 2014
%V 17
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2014__17_3_a3/
%G en
%F JIS_2014__17_3_a3
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/