shareshare link cite add Please grant OpenAIRE to access and update your ORCID works.This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

You have already added 0 works in your ORCID record related to the merged Research product.

# A new family of positive integers

Let n,p,k be three positive integers. We prove that the numbers binomial (n,k) 3F2 (1-k, -p, p-n ; 1, 1-n ; 1) are positive integers which generalize the classical binomial coefficients. We give two generating functions for these integers, and a straightforward application.

Comment: Enlarged version, LaTeX, 7 pages

ACM Computing Classification System: ComputingMilieux_MISCELLANEOUS

Microsoft Academic Graph classification: Hypergeometric function Binomial coefficient Combinatorics Discrete mathematics Mathematics

[INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], Discrete Mathematics and Combinatorics, Combinatorics (math.CO), FOS: Mathematics, 05A10 (Primary), 33C20 (Secondary), Mathematics - Combinatorics

[INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], Discrete Mathematics and Combinatorics, Combinatorics (math.CO), FOS: Mathematics, 05A10 (Primary), 33C20 (Secondary), Mathematics - Combinatorics

ACM Computing Classification System: ComputingMilieux_MISCELLANEOUS

Microsoft Academic Graph classification: Hypergeometric function Binomial coefficient Combinatorics Discrete mathematics Mathematics

- University of Marne la Vallée France
- Université Paris Diderot France

[1] M. Lassalle, Une identit´e en th´eorie des partitions, Journal of Combinatorial Theory, Series A, 89 (2000), 270-288. [OpenAIRE]

[2] M. Lassalle, Some combinatorial conjectures for Jack polynomials, Ann. Combin. 2 (1998), 61-83.

[3] M. Lassalle, Some combinatorial conjectures for shifted Jack polynomials, Ann. Combin. 2 (1998), 145-163.

[4] E. D. Rainville, Special functions, Chelsea, New York (1971).

[5] Jiang Zeng, A bijective proof of Lassalle's partition identity, Journal of Combinatorial Theory, Series A, 89 (2000), 289-290. [OpenAIRE]

Let n,p,k be three positive integers. We prove that the numbers binomial (n,k) 3F2 (1-k, -p, p-n ; 1, 1-n ; 1) are positive integers which generalize the classical binomial coefficients. We give two generating functions for these integers, and a straightforward application.

Comment: Enlarged version, LaTeX, 7 pages