A245791 Number of preferential arrangements of n labeled elements when at least k=6 elements per rank are required.

1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 925, 3433, 9439, 22881, 51767, 112269, 17390049, 140166497, 749266977, 3311021321, 13091222301, 48138992687, 2477067794573, 33549609515571, 292811657874791, 2040445353211231, 12382874543793451, 68436110449556971

Offset

0,13

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Formula

E.g.f.: 1/(2 + x - exp(x) + x^2/2! + x^3/3! + x^4/4! + x^5/5!). - Vaclav Kotesovec, Aug 02 2014

a(n) ~ n! / ((1+r^5/5!) * r^(n+1)), where r = 2.77092853312194416389... is the root of the equation 2 + r - exp(r) + r^2/2! + r^3/3! + r^4/4! + r^5/5! = 0. - Vaclav Kotesovec, Aug 02 2014

Maple

a:= proc(n) option remember; `if`(n=0, 1,
       add(a(n-j)*binomial(n, j), j=6..n))
    end:
seq(a(n), n=0..35);

Mathematica

CoefficientList[Series[1/(2 + x - E^x + x^2/2! + x^3/3! + x^4/4! + x^5/5!), {x, 0, 30}], x]*Range[0, 30]! (* Vaclav Kotesovec, Aug 02 2014 *)

Crossrefs

Cf. column k=6 of A245732.

Sequence in context: A066741 A325141 A244169 * A229641 A147548 A116989

Adjacent sequences: A245788 A245789 A245790 * A245792 A245793 A245794

Keyword

nonn

Author

Alois P. Heinz, Aug 01 2014

Status

approved