A245856 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 3.

1, 0, 0, 20, 70, 112, 1848, 12840, 62700, 591800, 5484908, 40589276, 421291780, 4704380800, 46345716880, 533446290384, 6931113219780, 85313661653400, 1121432682942740, 16310909250477380, 237534778732260548, 3578871132644512672, 57980168196079811800

Offset: 3

Author

Alois P. Heinz, Aug 04 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..400

Crossrefs

Column k=3 of A245733.

Cf. A102233, A232475, A245732.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1,
      add(b(n-j, k)*binomial(n, j), j=k..n))
    end:
a:= n-> b(n, 3) -b(n, 4):
seq(a(n), n=3..30);

Mathematica

With[{nn=30},CoefficientList[Series[1/(2-Exp[x]+x+x^2/2)-1/(2-Exp[x]+ x+ x^2/2+ x^3/6),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 14 2016 *)

Formula

E.g.f.: 1/(2-exp(x)+x+x^2/2)-1/(2-exp(x)+x+x^2/2+x^3/6).

a(n) = A102233(n) - A232475(n) = A245732(n,3) - A245732(n,4).