  A well-known result from Hardy and Ramanujan gives an asymptotic expression
for the number of possible ways to express an integer as the sum of smaller
integers. In this vein, we consider the general partitioning problem of writing
an integer $n$ as a sum of summands from a given sequence $\gL$ of
non-decreasing integers. Under suitable assumptions on the sequence $\gL$, we
obtain results using associated zeta-functions and saddle-point techniques. We
also calculate higher moments of the sequence $\gL$ as well as the expected
number of summands. Applications are made to various sequences, including those
of Barnes and Epstein types. These results are of potential interest in
statistical mechanics in the context of Bose-Einstein condensation.
