2016 UNCO Math Contest II Problems/Problem 8
Each circle in this tree diagram is to be assigned a value, chosen from a set , in such a way that along every pathway down the tree, the assigned values never increase. That is, , and . (It is permissible for a value in to appear more than once.)
(a) How many ways can the tree be so numbered, using only values chosen from the set ?
(b) Generalize to the case in which . Find a formula for the number of ways the tree can be numbered.
For maximal credit, express your answer in closed form as an explicit algebraic expression in .
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