An identity for generalized Pascal’s triangles. (English) Zbl 0607.05003

Volk, Wolfgang

Math. Educ. 20, 45-48 (1986).

This paper is concerned with an identity for adjacent coefficients of generalized Pascal’s triangles. This identity permits the construction of an arbitrary row of one of this schemes separately, which means that the preceding rows need not be computed. This result is extended to Pascal’s pyramids.

MSC:

05A10	Factorials, binomial coefficients, combinatorial functions
05A19	Combinatorial identities, bijective combinatorics
05-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics

Keywords:

generalized Pascal’s triangles; Pascal’s pyramids