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 of non-decreasing integers. Under suitable assumptions on the sequence , we obtain results using associated zeta-functions and saddle-point techniques. We also calculate higher moments of the sequence as well as

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... 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.