Python Math: nth Catalan Number
Python Math: Exercise-25 with Solution
Write a Python program for the nth Catalan numbers.
In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. They are named after the Belgian mathematician Eugène Charles Catalan (1814–1894).
Using zero-based numbering, the nth Catalan number is given directly in terms of binomial coefficients by
The first Catalan numbers for n = 0, 1, 2, 3, … are
1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, ....
The C5 = 42 noncrossing partitions of a 5-element set (below, the other 10 of the 52 partitions)
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def catalan_number(num): if num <=1: return 1 res_num = 0 for i in range(num): res_num += catalan_number(i) * catalan_number(num-i-1) return res_num for n in range(10): print(catalan_number(n))
1 1 2 5 14 42 132 429 1430 4862
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