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a(n) = floor( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).
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%I #13 Jan 05 2024 21:19:26

%S 1,0,1,1,2,2,5,7,14,21,42,66,132,214,429,715,1430,2431,4862,8398,

%T 16796,29393,58786,104006,208012,371450,742900,1337220,2674440,

%U 4847422,9694845,17678835,35357670,64822395,129644790,238819350,477638700,883631595,1767263190

%N a(n) = floor( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).

%D D. Miklos et al., eds., Combinatorics, Paul Erdős is Eighty, Bolyai Math. Soc., 1993, Vol. 1, p. 101.

%H G. C. Greubel, <a href="/A028303/b028303.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = floor(A001405(n)/A004526(n+3)). - _G. C. Greubel_, Jan 04 2024

%t Table[Floor[Binomial[n,Floor[n/2]]/Floor[(n+3)/2]], {n,0,50}] (* _G. C. Greubel_, Jan 04 2024 *)

%o (Magma) [Floor(Binomial(n,Floor(n/2))/Floor((n+3)/2)): n in [0..50]]; // _G. C. Greubel_, Jan 04 2024

%o (SageMath) [int(binomial(n,int(n/2))/((n+3)//2)) for n in range(51)] # _G. C. Greubel_, Jan 04 2024

%Y Cf. A000108, A001405, A004526.

%K nonn

%O 0,5

%A _N. J. A. Sloane_