SP106 BINSTIRL - Binary Stirling Numbers

The Stirling number of the second kind S(n, m) stands for the number of ways to partition a set of n things into m nonempty subsets. For example, there are seven ways to split a four-element set into two parts: {1, 2, 3} u {4}, {1, 2, 4} u {3}, {1, 3, 4} u {2}, {2, 3, 4} u {1}, {1, 2} u {3, 4}, {1, 3} u {2, 4}, {1, 4} u {2, 3}. There is a recurrence which allows you to compute S(n, m) for all m and n. S(0, 0) = 1, S(n, 0) = 0, for n > 0, S(0, m) = 0, for m > 0, S(n, m) = m\*S(n-1, m) + S(n-1, m-1), for n, m > 0. Your task is much "easier". Given integers n and m satisfying 1

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