A245792 Number of preferential arrangements of n labeled elements when at least k=7 elements per rank are required.

1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 3433, 12871, 35751, 87517, 199785, 436697, 927657, 401005793, 3296326113, 17887397621, 80157730101, 321127444171, 1195366208091, 4226755326331, 486914893507831, 6899197122043711, 61532746814157691, 436349292456987871

Offset

0,15

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! + x^6/6!). - Vaclav Kotesovec, Aug 02 2014

a(n) ~ n! / ((1+r^6/6!) * r^(n+1)), where r = 3.161936258680679649... is the root of the equation 2 + r - exp(r) + r^2/2! + r^3/3! + r^4/4! + r^5/5! + r^6/6! = 0. - Vaclav Kotesovec, Aug 02 2014

Maple

a:= proc(n) option remember; `if`(n=0, 1,
       add(a(n-j)*binomial(n, j), j=7..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^6/6!), {x, 0, 40}], x]*Range[0, 40]! (* Vaclav Kotesovec, Aug 02 2014 *)

Crossrefs

Cf. column k=7 of A245732.

Sequence in context: A172913 A172708 A244170 * A046253 A031824 A254093

Adjacent sequences: A245789 A245790 A245791 * A245793 A245794 A245795

Keyword

nonn

Author

Alois P. Heinz, Aug 01 2014

Status

approved