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

3,4

Links

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

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).

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 *)

Crossrefs

Column k=3 of A245733.

Cf. A102233, A232475, A245732.

Sequence in context: A362053 A357921 A335557 * A053741 A303609 A052516

Adjacent sequences: A245853 A245854 A245855 * A245857 A245858 A245859

Keyword

nonn

Author

Alois P. Heinz, Aug 04 2014

Status

approved