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A232475 Number of preferential arrangements of n labeled elements when at least k=4 elements per rank are required. 11
1, 0, 0, 0, 1, 1, 1, 1, 71, 253, 673, 1585, 38149, 277707, 1402831, 5923503, 85577571, 937629969, 7475614341, 48939413477, 587610659505, 7906296686903, 87384175023995, 804959532778571, 9729015122635103, 144711323234918941, 2009073351016603121 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
LINKS
I. Mezo, Periodicity of the last digits of some combinatorial sequences, arXiv preprint arXiv:1308.1637 [math.CO], 2013.
FORMULA
E.g.f.: 1/(2 + x - exp(x) + x^2/2 + x^3/6). - Vaclav Kotesovec, Aug 02 2014
a(n) ~ n! / ((1+r^3/6) * r^(n+1)), where r = 1.97615974210650519398... is the root of the equation 2 + r - exp(r) + r^2/2 + r^3/6 = 0. - Vaclav Kotesovec, Aug 02 2014
a(0) = 1; a(n) = Sum_{k=4..n} binomial(n,k) * a(n-k). - Ilya Gutkovskiy, Feb 09 2020
MAPLE
b:= proc(n) b(n):= `if`(n=0, 1, add(b(n-j)/j!, j=4..n)) end:
a:= n-> n!*b(n):
seq(a(n), n=0..30); # Alois P. Heinz, Jul 29 2014
MATHEMATICA
CoefficientList[Series[1/(2 + x - E^x + x^2/2 + x^3/6), {x, 0, 20}], x]*Range[0, 20]! (* Vaclav Kotesovec, Aug 02 2014 *)
CROSSREFS
Cf. column k=4 of A245732.
Sequence in context: A123038 A325079 A142325 * A243579 A142013 A033240
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2013
EXTENSIONS
More terms from Alois P. Heinz, Jul 29 2014
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)