A006326 Total preorders.

1, 5, 24, 122, 680, 4155, 27776, 202084, 1592064, 13513825, 123025408, 1196165886, 12374422528, 135740585015, 1573990072320, 19239037403528, 247255523459072, 3333340694137725, 47039231504678912, 693488743931379010, 10661950808321949696, 170659875799127955955

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• G. Kreweras, Les préordres totaux compatibles avec un ordre partiel, Math. Sci. Humaines No. 53 (1976), 5-30.
• G. Kreweras, Les préordres totaux compatibles avec un ordre partiel, Math. Sci. Humaines No. 53 (1976), 5-30. (Annotated scanned copy)

Crossrefs

Cf. A000111, A079502.

Programs

Maple

# After Alois P. Heinz in A000111:
b := proc(u, o) option remember;
`if`(u + o = 0, 1, add(b(o - 1 + j, u - j), j = 1..u)) end:
a := n -> (n-2)*b(n-1, 1)/2: seq(a(n), n = 3..23); # Peter Luschny, Oct 27 2017

Mathematica

b[u_, o_] := b[u, o] = If[u+o == 0, 1, Sum[b[o-1+j, u-j], {j, 1, u}]];
a[n_] := (n-2) b[n-1, 1]/2;
Array[a, 22, 3] (* Jean-François Alcover, Jun 01 2019, from Maple *)

Extensions

More terms from Sean A. Irvine, Mar 12 2017