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A028304
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a(n) = ceiling( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).
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1
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1, 1, 1, 1, 2, 3, 5, 7, 14, 21, 42, 66, 132, 215, 429, 715, 1430, 2431, 4862, 8398, 16796, 29393, 58786, 104006, 208012, 371450, 742900, 1337220, 2674440, 4847423, 9694845, 17678835, 35357670, 64822395, 129644790, 238819350, 477638700, 883631595, 1767263190, 3282060210
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OFFSET
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0,5
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REFERENCES
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D. Miklos et al., eds., Combinatorics, Paul Erdős is Eighty, Bolyai Math. Soc., 1993, Vol. 1, p. 101.
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LINKS
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FORMULA
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MAPLE
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ceil(%) ;
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MATHEMATICA
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Table[Ceiling[(1/(Ceiling[n/2] + 1)) Binomial[n, Floor[n/2]]], {n, 0, 49}] (* Alonso del Arte, Oct 30 2019 *)
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PROG
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(Magma) [Ceiling(Binomial(n, Floor(n/2))/Floor((n+3)/2)): n in [0..50]]; // G. C. Greubel, Jan 05 2024
(SageMath) [ceil(binomial(n, int(n/2))/((n+3)//2)) for n in range(51)] # G. C. Greubel, Jan 05 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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