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A245792 Number of preferential arrangements of n labeled elements when at least k=7 elements per rank are required. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)