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Tag Archives: binomial coefficient

Following are the common definitions of Binomial Coefficients.  A binomial coefficient C(n, k) can be defined as the coefficient of Xk in the expansion of… Read More
Given a number n, find the number of ways to multiply n elements with an associative operation. Examples :  Input : 2 Output : 2… Read More
Given N, the row number of Pascal’s triangle(row starting from 0). Find the count of odd numbers in the N-th row of Pascal’s Triangle.Prerequisite: Pascal’s… Read More
Given three integers, A, X and n, the task is to print terms of below binomial expression series. (A+X)n = nC0AnX0 + nC1An-1X1 + nC2An-2X2 +….+… Read More
Given an array of n distinct elements, count total number of subsets. Examples:  Input : {1, 2, 3} Output : 8 Explanation: the array contain… Read More
Given a positive integer n. The task is to find the sum of square of Binomial Coefficient i.e nC02 + nC12 + nC22 + nC32 +… Read More
Given a positive integer n. The task is to find the sum of even indexed binomial coefficient. That is, nC0 + nC2 + nC4 + nC6… Read More
The Leibniz harmonic triangle is a triangular arrangement of unit fractions in which the outermost diagonals consist of the reciprocals of the row numbers and… Read More
Given a positive integer n. The task is to find the maximum coefficient term in all binomial coefficient. The binomial coefficient series is nC0, nC1, nC2, ….,… Read More
Given an integer max, print Binomial Coefficients table that prints all binomial coefficients B(m, x) where m and x vary from 0 to maxExample :  … Read More
In mathematics, particularly in matrix theory and combinatorics, the Pascal Matrix is an infinite matrix containing binomial coefficients as its elements. There are three ways… Read More
Given a positive integer n, the task is to find the sum of binomial coefficient i.enC0 + nC1 + nC2 + ……. + nCn-1 +… Read More
In combinatorial mathematics, the Lobb number Lm, n counts the number of ways that n + m open parentheses can be arranged to form the… Read More
In combinatorics, the Narayana numbers N(n, k), n = 1, 2, 3 …, 1 ≤ k ≤ n, form a triangular array of natural numbers,… Read More
Prerequisite – Generalized PnC Set 1 Combinatorial problems can be rephrased in several different ways, the most common of which is in terms of distributing… Read More