Partition function (number theory)

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, ... (sequence in the OEIS).

Approximation formulas exist that are faster to calculate than the exact formula given above.

In comparison, the generating function of the regular partition numbers P(n) has this identity with respect to the theta function:

The products in the brackets are the so called Pochhammer products and they are defined as follows:

Therefore those two formulas are valid for the synthesis of the number sequence P(n):