A006326 - OEIS

%I M3931 #28 Jun 01 2019 11:30:35

%S 1,5,24,122,680,4155,27776,202084,1592064,13513825,123025408,

%T 1196165886,12374422528,135740585015,1573990072320,19239037403528,

%U 247255523459072,3333340694137725,47039231504678912,693488743931379010,10661950808321949696,170659875799127955955

%N Total preorders.

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

%H G. Kreweras, <a href="http://www.numdam.org/item?id=MSH_1976__53__5_0">Les préordres totaux compatibles avec un ordre partiel</a>, Math. Sci. Humaines No. 53 (1976), 5-30.

%H G. Kreweras, <a href="/A019538/a019538.pdf">Les préordres totaux compatibles avec un ordre partiel</a>, Math. Sci. Humaines No. 53 (1976), 5-30. (Annotated scanned copy)

%p # After _Alois P. Heinz_ in A000111:

%p b := proc(u, o) option remember;

%p `if`(u + o = 0, 1, add(b(o - 1 + j, u - j), j = 1..u)) end:

%p a := n -> (n-2)*b(n-1, 1)/2: seq(a(n), n = 3..23); # _Peter Luschny_, Oct 27 2017

%t b[u_, o_] := b[u, o] = If[u+o == 0, 1, Sum[b[o-1+j, u-j], {j, 1, u}]];

%t a[n_] := (n-2) b[n-1, 1]/2;

%t Array[a, 22, 3] (* _Jean-François Alcover_, Jun 01 2019, from Maple *)

%Y Cf. A000111, A079502.

%K nonn

%O 3,2

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Mar 12 2017