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. (Formerly M4988 N2145)

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

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.

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

Adjacent sequences: A000480 A000481 A000482 * A000484 A000485 A000486

Keyword

nonn

Author

N. J. A. Sloane

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