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

Author

Alois P. Heinz, Aug 01 2014

Keywords

• nonn

Links

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

Crossrefs

Cf. column k=7 of A245732.

Programs

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 *)

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