Consider a set of n pairs of parentheses, arranged in some legal way
(possibly concatenated to each other). For example,
is an example of such an arrangement, with n=4. Each pair has a nesting level. Consider the value of the entire arrangement to be the product of the nesting levels. In our example, the value is 3*2*2*1=12. Let f(n) be the sum of the values of all possible arrangements of n pairs of parentheses. This month's riddle: find, with proof, a closed-form expression for f(n). |
List of solvers:Yuping Luo (6 November 17:09)Dan Dima (7 November 05:38) Naftali Peles (12 November 17:35) Wenqi Zhang (16 November 11:38) Radu-Alexandru Todor (16 November 13:00) Daniel Bitin (25 November 08:31) Andreas Stiller (25 November 23:35) Lorenz Reichel (27 November 23:32) |
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Enjoy!