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A047865
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Number of derangements of n where minimal cycle size is at least 4.
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7
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1, 0, 0, 0, 6, 24, 120, 720, 6300, 58464, 586656, 6384960, 76471560, 994831200, 13939507296, 209097854784, 3345235180560, 56866395720960, 1023601917024000, 19448577603454464, 388972171805410656, 8168409582839579520, 179704944537482689920
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OFFSET
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0,5
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REFERENCES
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H. S. Wilf, Generatingfunctionology, Academic Press, NY, 1990, p. 147, Eq. 5.2.9 (q=3).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 176, Eq. 5.2.9 (q=3).
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FORMULA
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a(n) = (n-1)*a(n-1) + (n-1)*(n-2)*(n-3)*a(n-4).
E.g.f.: A(x) = 1/(1-x)*exp(-x-x^2/2-x^3/3) = 1 + 6*x^4/4! + 24*x^5/5! + ... satisfies the differential equation A'(x) = x^3/(1-x)*A(x). - Peter Bala, Apr 18 2012
a(n) ~ n! * exp(-11/6). - Vaclav Kotesovec, Aug 13 2013
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MAPLE
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with(combstruct): ZL3:=[S, {S=Set(Cycle(Z, card>3))}, labeled]:
seq (count (ZL3, size=n), n=0..21); # Zerinvary Lajos, Sep 26 2007
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MATHEMATICA
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nn=20; Range[0, nn]!CoefficientList[Series[Exp[-x-x^2/2-x^3/3]/(1-x), {x, 0, nn}], x] (* Geoffrey Critzer, Nov 11 2012 *)
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CROSSREFS
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Cf. A038205, A000166.
Sequence in context: A354074 A293300 A293487 * A355285 A182083 A293049
Adjacent sequences: A047862 A047863 A047864 * A047866 A047867 A047868
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Definition adjusted by Steven Finch, Mar 10 2022
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STATUS
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approved
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