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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!). - Vaclav Kotesovec, Aug 02 2014
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a(n) ~ n! / ((1+r^8/8!) * r^(n+1)), where r = 3.93616250913523371282009... 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! = 0. - Vaclav Kotesovec, Aug 02 2014
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!). - Vaclav Kotesovec, Aug 02 2014
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, 0, 40}], x]*Range[0, 40]! (* Vaclav Kotesovec, Aug 02 2014 *)
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Alois P. Heinz, <a href="/A245794/b245794.txt">Table of n, a(n) for n = 0..400</a>
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*binomial(n, j), j=9..n))
end:
seq(a(n), n=0..40);
allocated for Alois P. Heinz
Number of preferential arrangements of n labeled elements when at least k=9 elements per rank are required.
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 48621, 184757, 520677, 1293293, 2993565, 6626669, 14233965, 29938871, 62040891, 228000637831, 1914395677411, 10597881432571, 48446119334191, 197900630004571, 750527665784311, 2700730064112181
0,19
Cf. column k=9 of A245732.
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nonn
Alois P. Heinz, Aug 01 2014
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allocated for Alois P. Heinz
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