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A245793 Number of preferential arrangements of n labeled elements when at least k=8 elements per rank are required. 4
1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 12871, 48621, 136137, 335921, 772617, 1700273, 3633105, 7607297, 9481216677, 78911366771, 433024685291, 1961914734031, 7943932891111, 29871106149031, 106624217245891, 366332387265871, 100783979161693411 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,17

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!). - Vaclav Kotesovec, Aug 02 2014

a(n) ~ n! / ((1+r^7/7!) * r^(n+1)), where r = 3.550140591759854453327299... 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! = 0. - Vaclav Kotesovec, Aug 02 2014

MAPLE

a:= proc(n) option remember; `if`(n=0, 1,

       add(a(n-j)*binomial(n, j), j=8..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^7/7!), {x, 0, 40}], x]*Range[0, 40]! (* Vaclav Kotesovec, Aug 02 2014 *)

CROSSREFS

Cf. column k=8 of A245732.

Sequence in context: A172560 A031805 A244171 * A251922 A184453 A233936

Adjacent sequences:  A245790 A245791 A245792 * A245794 A245795 A245796

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 01 2014

STATUS

approved

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Last modified May 6 19:52 EDT 2021. Contains 343586 sequences. (Running on oeis4.)