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Foreword
Cattleya number is a number of columns, sometimes in combination math problems
Cattleya number from 1 start bit (zero-th bit is 1) In general: 1,1,5,14, 42, 132, 429,1430 ....
For several Cattleya have a grid graph model, which can be important formula: (from other people because I oj the Pirates of the map so that [n, m], but should actually be [n, n] a)
For the above this figure, the come [n, n] but not beyond y = x is the number of programs is the number of n-th Cattleya,
That stack are explained, but a better intuitive understanding of FIG.
Come apparent [n, n] regardless of the number of cross-border programs are C (2n, n) species, then excluded, the conversion can be considered,
For each path across the y = x, the first part after the inversion symmetry along all beyond y = x + 1, to obtain an equivalent path,
These programs and the number of paths can be computed directly from (0,0) come to (n-1, n + 1), i.e., C (2n, n-1)
Is the valid number of paths C (2n, n) -C (2n, n-1), to obtain a first key formulas, i.e., f [n] = C (2n, n) - C (2n, n-1) ;
A the same time you can be called a question bzoj3907