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Xu, C.N. (2013) Operator Proof of Recurrence Formula of Stirling Number of the First Kind. Journal of Inner Mongolia University for the Nationalities (Natural Sciences), 4, 384-385.

has been cited by the following article:

• TITLE: Shape of Numbers and Calculation Formula of Stirling Numbers

  AUTHORS: Ji Peng

  KEYWORDS: Combinatorics, Shape of Numbers, Stirling Numbers, Congruence Formula

  JOURNAL NAME: Open Access Library Journal, Vol.7 No.3, March 23, 2020

  ABSTRACT: 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.