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A000483
Associated Stirling numbers: second-order reciprocal Stirling numbers (Fekete) a(n) = [[n, 3]]. The number of 3-orbit permutations of an n-set with at least 2 elements in each orbit.
7
15, 210, 2380, 26432, 303660, 3678840, 47324376, 647536032, 9418945536, 145410580224, 2377609752960, 41082721413120, 748459539843840, 14345340443665920, 288650580508961280, 6085390148673177600, 134167064248901376000, 3088040233895705088000, 74077507611407752704000, 1849221425299053367296000
OFFSET
6,1
REFERENCES
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).
LINKS
A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 (1994), 771-778.
FORMULA
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
MATHEMATICA
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 *)
CROSSREFS
Cf. A000907, A001784, A001785. A diagonal of triangle in A008306.
Cf. A000276.
Sequence in context: A019553 A234249 A112496 * A162785 A076139 A163091
KEYWORD
nonn
EXTENSIONS
More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000
More terms from Sean A. Irvine, Nov 14 2010
STATUS
approved