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=. For-n, Consequently the poset P has the following binomial and Sheffer factorial functions. (i) B(k) = k! for 1 ? k ? 2m, and B(2m + 1) = ?(2m + 1)!, ii) D(1) = 1, D(k) = 2(k ? 1)! for 2 ? k ? 2m + 1, and D(2m + 2) = 2?

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