A245858 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 5.

1, 0, 0, 0, 0, 252, 924, 1584, 2574, 4004, 762762, 6062784, 31868200, 121314312, 399096216, 12936646128, 167685283332, 1429020461484, 9754485257594, 55756633204272, 905519956068420, 14816352889289380, 179362257853420980, 1745771827872126600

Offset

5,6

Links

Alois P. Heinz, Table of n, a(n) for n = 5..400

Formula

E.g.f.: 1/(1-Sum_{j>=5} x^j/j!) - 1/(1-Sum_{j>=6} x^j/j!).

a(n) = A245790(n) - A245791(n) = A245732(n,5) - A245732(n,6).

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, 5) -b(n, 6):
seq(a(n), n=5..30);

Crossrefs

Column k=5 of A245733.

Cf. A245790, A245791, A245732.

Sequence in context: A242570 A046379 A250794 * A200884 A275316 A275315

Adjacent sequences: A245855 A245856 A245857 * A245859 A245860 A245861

Keyword

nonn

Author

Alois P. Heinz, Aug 04 2014

Status

approved