Implications of Spivey’s Bell Number Formula
نویسندگان
چکیده
Note that B(n) is the n Bell number while S(n, k) is the Stirling number of the second kind. We have translated Spivey’s notation into Riordan’s familiar notation which we find more preferable in our work [5, 6]. The purpose of this note is to offer a short generating function proof of Equation (1). We discuss this proof in Section 2. We also use Spivey’s formula, in conjunction with the Stirling numbers of the first kind, to find a new double sum expression for B(n).
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