A245855 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 2.

1, 0, 6, 20, 120, 672, 5516, 40140, 368640, 3521870, 37445298, 422339502, 5215454426, 68144100780, 954428684280, 14160968076584, 222769496190060, 3692874342747114, 64493471050666430, 1181830474135532130, 22692074431844298558, 455404848204906308984

Offset

2,3

Links

Alois P. Heinz, Table of n, a(n) for n = 2..400

Formula

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

a(n) = A032032(n) - A102233(n) = A245732(n,2) - A245732(n,3).

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, 2) -b(n, 3):
seq(a(n), n=2..25);

Crossrefs

Column k=2 of A245733.

Cf. A032032, A102233, A245732.

Sequence in context: A267855 A099840 A223045 * A074012 A074013 A333896

Adjacent sequences: A245852 A245853 A245854 * A245856 A245857 A245858

Keyword

nonn

Author

Alois P. Heinz, Aug 04 2014

Status

approved