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A028304 a(n) = ceiling( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).

%I A028304 #26 Jan 05 2024 04:43:32
%S A028304 1,1,1,1,2,3,5,7,14,21,42,66,132,215,429,715,1430,2431,4862,8398,
%T A028304 16796,29393,58786,104006,208012,371450,742900,1337220,2674440,
%U A028304 4847423,9694845,17678835,35357670,64822395,129644790,238819350,477638700,883631595,1767263190,3282060210
%N A028304 a(n) = ceiling( binomial(n, floor(n/2))/(1 + ceiling(n/2)) ) (interpolates between Catalan numbers).
%D A028304 D. Miklos et al., eds., Combinatorics, Paul Erdős is Eighty, Bolyai Math. Soc., 1993, Vol. 1, p. 101.
%H A028304 G. C. Greubel, <a href="/A028304/b028304.txt">Table of n, a(n) for n = 0..1000</a>
%F A028304 a(2*n) = A000108(n), a(2*n+1) = A130380(n+1). - _R. J. Mathar_, Dec 15 2015
%F A028304 a(n) = ceiling(A001405(n)/A004526(n+3)). - _G. C. Greubel_, Jan 05 2024
%p A028304 A028304 := proc(n)
%p A028304     A001405(n)/(ceil(n/2)+1) ;
%p A028304     ceil(%) ;
%p A028304 end proc: # _R. J. Mathar_, Dec 15 2015
%t A028304 Table[Ceiling[(1/(Ceiling[n/2] + 1)) Binomial[n, Floor[n/2]]], {n, 0, 49}] (* _Alonso del Arte_, Oct 30 2019 *)
%o A028304 (Magma) [Ceiling(Binomial(n,Floor(n/2))/Floor((n+3)/2)): n in [0..50]]; // _G. C. Greubel_, Jan 05 2024
%o A028304 (SageMath) [ceil(binomial(n,int(n/2))/((n+3)//2)) for n in range(51)] # _G. C. Greubel_, Jan 05 2024
%Y A028304 Cf. A000108, A000245, A001405, A004526, A130380.
%K A028304 nonn
%O A028304 0,5
%A A028304 _N. J. A. Sloane_