central binomial coefficient
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Input
$$N=3$$
Solution
$$Central\ Binomial\ Cofficient =20$$
Formula
Given an integer N, the task is to find the \(N^{th}\) Central binomial coefficient The first few Central binomial coefficients for \(N = 0, 1, 2, 3..\) are Example: Central Binomial Cofficient $$=\frac{2*N}{N}=\frac{2*3}{3}=\frac{6*5*4}{3*2*1}=20$$
What is Central binomial coefficient and Catalan Number?
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What is Central binomial coefficient and Catalan Number?
The focal binomial coefficients are defined by
(n= 0,1,...,) and are firmly identified with the Catalan numbers
Many realities about these coefficients and Catalan numbers can be found in the new book of Koshy. Henry Gould has gathered various personalities including focal binomial coefficients in and a huge rundown of references on Catalan numbers in Riordan's book is likewise a decent reference.
Our center here will associate with power arrangement including these numbers. A few fascinating forces arrangements with focal binomial coefficients were acquired and talked about by Lehmer.
Different models were given by We in zierl and Zucker. Hansen's Table [8] contains such arrangements as well, for example, passages (5.9.23),(5.18.9), (5.24.15), (5.24.30), (5.25.7), (5.27.9), (5.27.12), (5.27.17). The producing elements of the numbers 2nn and Cn are notable, [8, (5.24.15)],
For both arrangements we need |4x|<1. The arrangement (2) follows effectively from (1) by joining. In this note, we present a technique for producing power arrangement including focal binomial coefficients by using fitting binomial changes.
Our outcomes incorporate a few fascinating force series where the coefficients are results of focal binomial coefficients and symphonious numbers Hn, and furthermore results of Catalan numbers and consonant numbers.
As usual,
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