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Definition and examples

For a positive integer , is the number of distinct ways of representing as a sum of positive integers. For the purposes of this definition, the order of the terms in the sum is irrelevant: two sums with the same terms in a different order (e.g., and ) are not considered distinct.

By convention , as there is one way of representing 0 as a sum of positive integers (the empty sum). Furthermore when is negative.

The

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