In 1838, the Belgian mathematician Eugene C. Catalan (1814-1894) discovered that the number C_n of well-formed sequences, with n pairs of left and right parentheses, is given by C_n=1+1(2n)), where n ≥0 [1, 2].For example, there are exactly five well-formed sequences with three pairs of left and right parentheses: ()()(), ()(()), (())(), (()()), ((())). The case n = 0 yields the null sequence, often denoted by λ. Notice that ()) and ((()()), for example, are not correctly parenthesised.
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机译:1838年,比利时数学家Eugene C. Catalan(1814-1894)发现,具有n对左右括号的格式良好的序列数C_n由C_n = 1 / n + 1(2n / n)给出),其中n≥0[1、2]。例如,正好有五个格式正确的序列,带有三对左右括号:()()(),()(()),(()) (),(()()),((()))。 n = 0的情况下会产生空序列,通常用λ表示。请注意,例如,())和(((()()))没有正确地加上括号。
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