Balanced parentheses

How many ways can 44 pairs of parentheses be arranged so that every prefix has at least as many "(" as ")"?

Show hints (2)+
  1. Valid bracket sequences are counted by the Catalan numbers.
  2. Cn=1n+1(2nn)C_n = \tfrac{1}{n+1}\binom{2n}{n}.

Answer

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14

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Asked at: Jane Street, Two Sigma

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