A245795 Number of preferential arrangements of n labeled elements when at least k=10 elements per rank are required.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 184757, 705433, 1998725, 4992289, 11618957, 25852921, 55791791, 117832681, 245039011, 503891821, 5552024604991, 46933238932021, 261680950107511, 1205121760579981, 4959685199012641, 18947093053200193

Offset

0,21

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! + x^7/7! + x^8/8! + x^9/9!). - Vaclav Kotesovec, Aug 02 2014

a(n) ~ n! / ((1+r^9/9!) * r^(n+1)), where r = 4.320434975980068857383128... 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! + r^7/7! + r^8/8! + r^9/9! = 0. - Vaclav Kotesovec, Aug 02 2014

Maple

a:= proc(n) option remember; `if`(n=0, 1,
       add(a(n-j)*binomial(n, j), j=10..n))
    end:
seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[1/(2 + x - E^x + x^2/2! + x^3/3! + x^4/4! + x^5/5! + x^6/6! + x^7/7! + x^8/8! + x^9/9!), {x, 0, 40}], x]*Range[0, 40]! (* Vaclav Kotesovec, Aug 02 2014 *)

Crossrefs

Cf. column k=10 of A245732.

Sequence in context: A245863 A140933 A244173 * A251449 A131908 A234409

Adjacent sequences: A245792 A245793 A245794 * A245796 A245797 A245798

Keyword

nonn

Author

Alois P. Heinz, Aug 01 2014

Status

approved