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A245790
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Number of preferential arrangements of n labeled elements when at least k=5 elements per rank are required.
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8
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1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 253, 925, 2509, 6007, 13443, 785643, 6114551, 31980469, 138704361, 539262713, 13685913105, 170996304653, 1442111683785, 9802624250281, 58233700998845, 939069565583991, 15109164547164171, 181402703206632211, 1758154702415920051
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OFFSET
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0,11
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LINKS
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FORMULA
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E.g.f.: 1/(2 + x - exp(x) + x^2/2! + x^3/3! + x^4/4!). - Vaclav Kotesovec, Aug 02 2014
a(n) ~ n! / ((1+r^4/4!) * r^(n+1)), where r = 2.376178375424367122... is the root of the equation 2 + r - exp(r) + r^2/2! + r^3/3! + r^4/4! = 0. - Vaclav Kotesovec, Aug 02 2014
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*binomial(n, j), j=5..n))
end:
seq(a(n), n=0..30);
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MATHEMATICA
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CoefficientList[Series[1/(2 + x - E^x + x^2/2! + x^3/3! + x^4/4!), {x, 0, 30}], x]*Range[0, 30]! (* Vaclav Kotesovec, Aug 02 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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