Asymptotics for Lacunary sums of binomial coefficients and a card problem with ranks.

Lengyel, Tamás

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The Catalan Numbers. Part II 1

Karol Pąk (2006)

Formalized Mathematics

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In this paper, we define sequence dominated by 0, in which every initial fragment contains more zeroes than ones. If n ≥ 2 · m and n > 0, then the number of sequences dominated by 0 the length n including m of ones, is given by the formula [...] and satisfies the recurrence relation [...] Obviously, if n = 2 · m, then we obtain the recurrence relation for the Catalan numbers (starting from 0) [...] Using the above recurrence relation we can see that [...] where [...] and hence [...]...