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Internet Message Format  |  1993-01-04  |  937 b 
  1. Path: sparky!uunet!think.com!sdd.hp.com!ux1.cso.uiuc.edu!roundup.crhc.uiuc.edu!focus!hougen
  2. From: hougen@focus.csl.uiuc.edu (Darrell Roy Hougen)
  3. Newsgroups: sci.math
  4. Subject: Generalization of binomial theorem wanted
  5. Date: 4 Jan 1993 05:26:46 GMT
  6. Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
  7. Lines: 14
  8. Message-ID: <1i8hqmINN1lf@roundup.crhc.uiuc.edu>
  9. NNTP-Posting-Host: focus.csl.uiuc.edu
  10. Summary: Generalization of binomial theorem wanted
  11. Keywords: binomial
  12.  
  13. In terms of m and n, how many unique terms are there in
  14.     (x_1 + x_2 + ... + x_m)^n
  15. when it is expanded?
  16.  
  17. I have a rather cumbersome formula and I'm looking for something more
  18. concise.  This must be a FAQ but it wasn't in the sci.math FAQ file.
  19.  
  20. The formula I have is
  21.  
  22.                 n 
  23.             sum                 sum                 1  
  24.             i = 1    k_1 <= k_2 <= ... <= k_i <= m
  25.  
  26. Darrell R. Hougen
  27.