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A245791 Number of preferential arrangements of n labeled elements when at least k=6 elements per rank are required. 4
1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 925, 3433, 9439, 22881, 51767, 112269, 17390049, 140166497, 749266977, 3311021321, 13091222301, 48138992687, 2477067794573, 33549609515571, 292811657874791, 2040445353211231, 12382874543793451, 68436110449556971 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,13
LINKS
FORMULA
E.g.f.: 1/(2 + x - exp(x) + x^2/2! + x^3/3! + x^4/4! + x^5/5!). - Vaclav Kotesovec, Aug 02 2014
a(n) ~ n! / ((1+r^5/5!) * r^(n+1)), where r = 2.77092853312194416389... is the root of the equation 2 + r - exp(r) + r^2/2! + r^3/3! + r^4/4! + r^5/5! = 0. - Vaclav Kotesovec, Aug 02 2014
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*binomial(n, j), j=6..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, 0, 30}], x]*Range[0, 30]! (* Vaclav Kotesovec, Aug 02 2014 *)
CROSSREFS
Cf. column k=6 of A245732.
Sequence in context: A066741 A325141 A244169 * A229641 A147548 A116989
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 01 2014
STATUS
approved

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Last modified April 15 04:34 EDT 2024. Contains 371667 sequences. (Running on oeis4.)