| 一类组合和式的性质与应用 |
| |
| 引用本文： | 孟凡申.一类组合和式的性质与应用[J].山西师范大学学报,2009,23(2):37-42. |
| |
| 作者姓名： | 孟凡申 |
| |
| 作者单位： | 浙江工业大学浙西分校数理系,浙江,衢州,324000
|
| |
| 摘 要： | 设k,n,r∈N,记F（r,n,k）=∑ri=0（-1）r-inr-iik,证明了F（r,n,k）的若干性质,推出了F（r,n,k）的4个递推关系式和5个关系式,得到了公式F（n＋h,n,n＋k）=∑hr=0hr（n＋r）!∑k-ri=0s（ik-r）k＋nk-r＋i和F（n,n＋h,k）=∑nr=1（-1）n-rh-1＋n-rn-rr!∑k-ri=0si（k-r）kk-r＋i（k〉0）,其中（s（ik））=is（ik-1）＋（k＋i-1）si（-k1-1）（1≤i≤k）.还导出了重要公式F（r,n,n）＋F（n-r,n,n）=n!（0≤r≤n）.
|
| 关 键 词： | 组合和式 递推关系式 计算公式 特殊值 |
Properties and Application of a Certain Combinatorial Sum |
| |
| MENG Fan-shen.Properties and Application of a Certain Combinatorial Sum[J].Journal of Shanxi Teachers University,2009,23(2):37-42. |
| |
| Authors: | MENG Fan-shen |
| |
| Institution: | Department of Mathematics and Physics;West Branch of Zhejiang University of Technology;Quzhou 324000;Zhejiang;China |
| |
| Abstract: | In this paper,k,n,r∈N,and F（r,n,k）=ri=0（-1）r-inr-iik,we prove some properties of F（r,n,k）,derive its 4 recurrence relations and 5 other relations,get the formulas F（n＋h,n,n＋k）=hr=0hr（n＋r）k-ri=0sk-rik＋nk-r＋i and F（n,n＋h,k）=nr=1（-1）n-rh-1＋n-rn-rrk-ri=0sk-rikk-r＋i（k〉0）,where s（k）i=is（k-1）i＋（k＋i-1）s（k-1）i-1（1≤i≤k）.We also deduce an important formula F（r,n,n）＋F（n-r,n,n）=n（0≤r≤n）. |
| |
| Keywords: | combinatorial sum recurrence relations calculation formula special value |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
