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A000483
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Associated Stirling numbers: second order reciprocal Stirling numbers (Fekete) [[n, 3]]. The number of 3-orbit permutations of an n-set with at least 2 elements in each orbit.
(Formerly M4988 N2145)
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7
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15, 210, 2380, 26432, 303660, 3678840, 47324376, 647536032, 9418945536, 145410580224, 2377609752960, 41082721413120, 748459539843840, 14345340443665920, 288650580508961280, 6085390148673177600, 134167064248901376000, 3088040233895705088000, 74077507611407752704000, 1849221425299053367296000
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OFFSET
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6,1
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 75.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 6..200
A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 (1994), 771-778.
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FORMULA
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With alternating signs: Ramanujan polynomials psi_4(n-3, x) evaluated at 1. - Ralf Stephan, Apr 16 2004
E.g.f.: -((x+log(1-x))^3)/6. - Vladeta Jovovic, May 03 2008
Conjecture: (n-2)*(n-4)*a(n) -(n-1)*(3*n^2-21*n+35)*a(n-1) +(n-1)*(n-2)*(3*n^2-24*n+47)*a(n-2) -(n-5)*(n-1)*(n-2)*(n-3)*(n-4)*a(n-3)=0. - R. J. Mathar, Jul 18 2015
Conjecture: 3*(-n+4)*a(n) +(9*n^2-59*n+90)*a(n-1) +(-9*n^3+96*n^2-348*n+436)*a(n-2) +(n-3)*(3*n^3-45*n^2+237*n-430)*a(n-3) +5*(n-5)*(n-6)*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Jul 18 2015
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MATHEMATICA
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nn=25; a=Log[1/(1-x)]-x; Drop[Range[0, nn]!CoefficientList[Series[a^3/3!, {x, 0, nn}], x], 6] (* Geoffrey Critzer, Nov 03 2012 *)
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CROSSREFS
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Cf. A000907, A001784, A001785. A diagonal of triangle in A008306.
Cf. A000276.
Sequence in context: A019553 A234249 A112496 * A162785 A076139 A163091
Adjacent sequences: A000480 A000481 A000482 * A000484 A000485 A000486
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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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More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000
More terms from Sean A. Irvine, Nov 14 2010
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STATUS
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approved
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