A366108 a(n) = floor(binomial(n-1, floor((n-1)/2))/2).

1, 1, 3, 5, 10, 17, 35, 63, 126, 231, 462, 858, 1716, 3217, 6435, 12155, 24310, 46189, 92378, 176358, 352716, 676039, 1352078, 2600150, 5200300, 10029150, 20058300, 38779380, 77558760, 150270097, 300540195, 583401555, 1166803110, 2268783825, 4537567650, 8836315950

Offset: 3

Author

Stefano Spezia, Sep 29 2023

Keywords

• nonn

Links

• Gábor Czédli, Minimum-sized generating sets of the direct powers of the free distributive lattice on three generators and a Sperner theorem, arXiv:2309.13783 [math.CO], 2023. See formulas (3.6) at p. 4 and (4.15) at p. 8.

Crossrefs

Cf. A001405, A004526, A218708, A335322, A366107, A366109.

Programs

Mathematica

a[n_]:=Floor[Binomial[n-1,Floor[(n-1)/2]]/2]; Array[a,36,3]

PARI

a(n) = binomial(n-1, (n-1)\2)\2; \\ Michel Marcus, Sep 30 2023

Formula

a(n)/A366107(n) ~ 7/4 (see Remark 3.4 at p. 5 in Czédli).

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