%I #9 Oct 03 2023 10:01:59

%S 1,1,2,4,7,13,26,46,92,168,333,616,1225,2288,4558,8580,17107,32413,

%T 64664,123170,245832,470288,938943,1802770,3600207,6933733,13849778,

%U 26744400,53429368,103411680,206621384,400720260,800747232,1555737480,3109074130,6050090200,12091800773

%N a(n) = floor(n!*(3*floor(n/2)!*ceiling(n/2)! + 3*floor((n+2)/2)!*ceiling((n-2)/2)! - 6*floor(n/2)!*ceiling((n-2)/2)!)^(-1)).

%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) ~ 7/6 (see Remark 3.4 at p. 5 in Czédli).

%F a(n) ~ c*2^n/sqrt(n), with c = 1/(3*sqrt(2*Pi)) = (2/3)*A218708.

%t a[n_]:=Floor[n!(3Floor[n/2]!Ceiling[n/2]! + 3Floor[(n+2)/2]!Ceiling[(n-2)/2]! - 6Floor[n/2]!Ceiling[(n-2)/2]!)^(-1)]; Array[a,37,3]

%Y Cf. A000142, A004526, A081123, A218708, A366107, A366108.

%K nonn

%O 3,3

%A _Stefano Spezia_, Sep 29 2023