Triangles of numbers

triangular array of the binomial coefficients in mathematics

family of positive integers that occur as coefficients in the binomial theorem

conjecture on the pattern of forward differences of the sequence of prime numbers

number of ways to partition a set of n objects into k non-empty subsets

number of permutations of the numbers from 1 to n in which m elements are greater than the previous element

triangular arrangement L(r,c) of unit fractions, where (r,c) are row and column numbers, such that L(r, 1) = 1/r and L(r, c) = L(r − 1, c − 1) − L(r, c − 1)

number of permutations of n elements with k disjoint cycles

number of paths between grid corners, allowing diagonal steps

numbers giving a solution to several counting problems in combinatorics

three-dimensional arrangement of the trinomial numbers, which are the coefficients of the trinomial expansion and the trinomial distribution

right-angled triangular array of natural numbers, used in computer science education

conjecture in combinatorial number theory

mathematical sequence

infinite matrices with Pascal's triangle as elements

triangular arrangement of numbers based on the Fibonacci numbers

triangle of numbers analogous to Pascal's triangle

mathematical concept

doubly indexed sequence of numbers, polynomials, etc., in which each row is only as long as the row's own index

array of partial sums of the binomial coefficients

triangular array of the trinomial coefficients in mathematics