A245854 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 1.

1, 2, 12, 68, 520, 4542, 46550, 540136, 7045020, 101865410, 1619046418, 28053492348, 526430246264, 10636085523910, 230214619661790, 5314695463338704, 130356558777712468, 3385311352838750538, 92797887464933030762, 2677623216872061223780, 81123642038690958720048

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..400

Formula

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

a(n) = A000670(n) - A032032(n) = A245732(n,1) - A245732(n,2).

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, 1) -b(n, 2):
seq(a(n), n=1..25);

Crossrefs

Column k=1 of A245733.

Cf. A000670, A032032, A245732.

Sequence in context: A128103 A359489 A329789 * A078839 A243771 A026306

Adjacent sequences: A245851 A245852 A245853 * A245855 A245856 A245857

Keyword

nonn

Author

Alois P. Heinz, Aug 04 2014

Status

approved