%I #15 Oct 03 2023 10:01:45
%S 1,1,3,5,10,17,35,63,126,231,462,858,1716,3217,6435,12155,24310,46189,
%T 92378,176358,352716,676039,1352078,2600150,5200300,10029150,20058300,
%U 38779380,77558760,150270097,300540195,583401555,1166803110,2268783825,4537567650,8836315950
%N a(n) = floor(binomial(n-1, floor((n-1)/2))/2).
%H Gábor Czédli, <a href="https://arxiv.org/abs/2309.13783">Minimum-sized generating sets of the direct powers of the free distributive lattice on three generators and a Sperner theorem</a>, arXiv:2309.13783 [math.CO], 2023. See formulas (3.6) at p. 4 and (4.15) at p. 8.
%F a(n)/A366107(n) ~ 7/4 (see Remark 3.4 at p. 5 in Czédli).
%F a(n) ~ c*2^n/sqrt(n), with c = 1/(2*sqrt(2*Pi)) = A218708.
%t a[n_]:=Floor[Binomial[n-1,Floor[(n-1)/2]]/2]; Array[a,36,3]
%o (PARI) a(n) = binomial(n-1, (n-1)\2)\2; \\ _Michel Marcus_, Sep 30 2023
%Y Cf. A001405, A004526, A218708, A335322, A366107, A366109.
%K nonn
%O 3,3
%A _Stefano Spezia_, Sep 29 2023