In combinatorial mathematics the Catalan numbers form a sequence of natural numbers that occur in various counting problems often involving recursively defined objects. The first Catalan numbers for n 0 1.

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### They are named after the Belgian mathematician Eugène Charles Catalan 18141894.

**What is a sub n in arithmetic sequence**. N th Term or General Term of an Arithmetic Progressions. The nth Catalan number is given directly in terms of binomial coefficients by. In an AP with first term a and common difference d the n th termor the general term is given by a n a n 1d Note that an AP can be finite or infinite according to as the number of terms are finite or infinite.

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