One 、 Eric · Temple · bell

Bell number is a series of integers in combinatorics , With Eric · Temple · bell （Eric Temple Bell） name ,

Eric · Temple · bell （ Born in 1883 year 2 month 7 Japan , Aberdeen, Aberdeen, Scotland , On 1960 year 12 month 21 Died in Watsonville, California, USA on the th ）, Scottish American mathematician 、 Educators and writers , He has made great contributions to analytical number theory .

bell stay 19 Immigrated to the United States at the age of , And immediately enter Stanford University , Two years later, he got his bachelor's degree there . after 1908 Year's efforts , He received a master's degree from the University of Washington . Again , After another year of preparatory school , He is in 1912 He received his doctorate in mathematics from Columbia University in . In the last few years , Bell is married , Try to be a mule Skinner 、 Ranchers 、 surveyor 、 Work in teachers and other industries . Bell accepted the position of teaching mathematics at the University of Washington immediately after receiving his doctorate , He has been a professor of mathematics at the school , until 1926 He was appointed professor of mathematics at California Institute of technology at the age of . from 1931 Year to 1933 year , He is president of the American Mathematical Association .

bell Published about 250 An academic article . Because of his work 《 Arithmetic interpretation 》（1921 year ）, He is in 1924 received Bôcher prize . His two books 《 Algebraic arithmetic 》（1927 year ） and 《 The development of Mathematics 》（1940 year ） Become the standard in this field , The latter is used clearly 、 Concise language outlines what bell considers the most important mathematical trends .

bell Best known is his best seller , Such as 《 Mathematical man 》（1937） and 《 The queen of mathematics and the servant of Science 》（1951）. He also wrote Fermat's Last Theorem , Last question （1961 year ） The history of . These works , Especially in Mathematics , Although quite bizarre , Not always historically accurate , But it still attracts a wide range of readers . Bell to John · Tyne wrote a lot of science fiction under his pseudonym , Include 《 Time flow 》（1946 year ）.

Two 、 Calculation method and source program

Bell The definition of number ： The first n individual Bell A number represents a set {1,2,3,...,n} Number of partition schemes , namely ：B[0] = 1;

every last Bell Numbers are of the second kind Stirling Sum of numbers , namely ：

The second category Stirling The meaning of number is ：S(n,k) It means that you will n An object is divided into k A non empty, indistinguishable （ It can be understood that the box has no number ） The way to assemble

Count . Obviously , every last Bell Is the corresponding second kind Stirling Sum of the numbers .

using System;
using System.Text;
using System.Collections;
using System.Collections.Generic;

namespace Legalsoft.Truffer.Algorithm
{
    public static partial class Number_Sequence
    {
        /// <summary>
        ///  Bell count （Bell Number） The calculation method of 
        /// </summary>
        /// <param name="n"></param>
        /// <returns></returns>
        public static long Bell_Number(int n)
        {
            long[,] bell = new long[n + 1, n + 1];
            bell[0, 0] = 1;
            for (int i = 1; i <= n; i++)
            {
                bell[i, 0] = bell[i - 1, i - 1];
                for (int j = 1; j <= i; j++)
                {
                    bell[i, j] = bell[i - 1, j - 1] + bell[i, j - 1];
                }
            }
            return bell[n, 0];
        }
    }
}

————————————————————————

POWER BY TRUFFER.CN