By counting the same set in two ways, prove the following identity:
n ∑ k = 0 ( k m ) ( n k ) = ( n m ) 2 n − m . ∑k=0n(km)(nk)=(nm)2n−m. notes: for there is no meaning to the word "towers" other than what is given: ∅ ⊆ a ⊆ b ⊆ { 1 , 2 , … , n } .

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