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A245795 Number of preferential arrangements of n labeled elements when at least k=10 elements per rank are required. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 21 08:18 EDT 2021. Contains 345358 sequences. (Running on oeis4.)