This article investigated the idea of Shape of numbers and introduced new operators. The idea divides all products of k distinct integers in [1, n - 1] into 2K-1 catalogs and derives the calculation formula of every catalog. As a simple deduction, a direct formula of the Stirling numbers of the first kind S1(n, n - k) and a simple recursive formula of Stirling numbers of the second kind S2(n, n - k) are obtained. By analyzing the Shape of numbers, new congruence formulas are obtained.
Cite this paper
Peng, J. (2020). Shape of Numbers and Calculation Formula of Stirling Numbers. Open Access Library Journal, 7, e6081. doi: http://dx.doi.org/10.4236/oalib.1106081.
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