1 votes 1 votes How to find the coefficient ( for eg $x^7$ ) in the generating function$(1+x+x^2+x^3+..)(1+x^2+x^4+x^6+..)(1+x^5+x^{10}+x^{15}+..)$ ? Combinatory kenneth-rosen generating-functions discrete-mathematics counting + – anip asked Aug 15, 2018 edited Mar 4, 2019 by Pooja Khatri anip 505 views answer comment Share Follow See 1 comment See all 1 1 comment reply pankaj_vir commented Aug 15, 2018 reply Follow Share Check this: https://gateoverflow.in/217112/kennneth-rosen-chapter-counting 0 votes 0 votes Please log in or register to add a comment.
Best answer 0 votes 0 votes We can solve it in the following way. x7 will be generated in the following way (025,160,205,340,520,700) So the coefficient will be 6. In first series 0 - x0 In second series 2- x2 In third series 5- x5 shubham6596 answered Aug 15, 2018 selected Aug 17, 2018 by anip shubham6596 comment Share Follow See all 2 Comments See all 2 2 Comments reply anip commented Aug 16, 2018 reply Follow Share here why the combinations (421, 430) are not taken? 0 votes 0 votes shubham6596 commented Aug 16, 2018 reply Follow Share In 421 - x1 is not present int third bracket. So this combination is not possible. Similarly for 430 ->x^3 is not present in the second bracket. 1 votes 1 votes Please log in or register to add a comment.