%0 Journal Article
%T Shape of Numbers and Calculation Formula of Stirling Numbers
%A Ji Peng
%J Open Access Library Journal
%V 7
%N 3
%P 1-11
%@ 2333-9721
%D 2020
%I Open Access Library
%R 10.4236/oalib.1106081
%X 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 2<sup>K-1</sup> 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.
%K Combinatorics
%K Shape of Numbers
%K Stirling Numbers
%K Congruence Formula
%U http://www.oalib.com/paper/5426513