Function: numbpart
Section: combinatorics
C-Name: numbpart
Prototype: G
Help: numbpart(n): number of partitions of n.
Doc: gives the number of unrestricted partitions of
 $n$, usually called $p(n)$ in the literature; in other words the number of
 nonnegative integer solutions to $a+2b+3c+\cdots=n$. $n$ must be of type
 integer and $n<2^{54} \approx 1.8 E16$ (with trivial values $p(n) = 0$
 for $n < 0$ and $p(0) = 1$). The algorithm uses the
 Hardy-Ramanujan-Rademacher formula and runs in time $\tilde{O}(n)$, which is
 roughly quadratic in the output size. Note that a more complicated
 implementation of the formula would run in time $\tilde{O}(n^{1/2})$.

 To explicitly enumerate them, see \tet{partitions}.
