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母函数方法求出的,求论证。。。http://hi.baidu.com/sulipol/blog/item/0ace8af56765aad4f3d385ee.html 定义函数h(x)=g(pi^x)=(x+1)^3 为了简化函数,定义函数h(x)=g(pi^x)=(x+1)^3 求一个数n的每个因子的.因子个数的三次方的和的母函数如下: (h(0)*p1^0 + h(1)*p1^1 + ... + h(k1)*p1^k1)*...*( h(0)pi^0 + h(1)pi^1 + ... + h(i)pi^ki 这时总的方案数ss=(h(0)+h(1)+...+h(k1))*...*(h(1)+h(2)+...+h(ki)) 再利用求和公式1^3 + 2^3 + …… n^3 = [n (n+1) / 2]^2 可得ss=PI[(ki+1)(ki+2)/2]^2 ,(PI代表连乘符号) MORE:http://hi.baidu.com/sulipol/blog/item/0ace8af56765aad4f3d385ee.html Followed by: Post your reply here: |
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