[問題] Combinatorics

[pikahacker (Beat Cal)]

Start with a row containing all positive integers. Then delete every mth
column. Then replace the remaining entries by partial sums. Delete every
(m-1)st column. Then replace with partial sums again, and so on. Show that
the final result is a sequence of mth powers.

  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
  1   2   3   4       6   7   8   9      11  12  13  14
  1   3   6  10      16  23  31  40      51  63  76  90
  1   3   6          16  23  31          51  63  76
  1   4  10          26  49  80         131 194 270
  1   4              26  49             131 194
  1   5              31  80             211 405
  1                  31                 211
  1                  32                 243

  1^5                2^5                3^5

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