A182661 Expansion of x^3*exp(-x)/(3*(1-x)).

2, 0, 20, 80, 630, 4928, 44520, 444960, 4894890, 58738240, 763597692, 10690366960, 160355505310, 2565688083840, 43616697426640, 785100553677888, 14916910519881810, 298338210397633920, 6265102418350314980, 137832253203706926480

Offset

3,1

Comments

a(n) is the number of 3-cycles in all derangements of {1,2,...n}.

Links

Table of n, a(n) for n=3..22.

Formula

E.g.f.: x^3 * exp(-x)/(3*(1-x)).

In general, E.g.f. for the number of k cycles in the derangements of [n] is: x^k * exp(-x)/(k*(1-x)).

Maple

egf:= x^3 * exp(-x)/(3*(1-x)):
a:= n-> n! * coeff (series (egf, x, n+1), x, n):
seq (a(n), n=3..25);

Mathematica

Table[Count[Flatten[Map[Length, Map[ToCycles, Derangements[n]], {2}]], 3], {n, 0, 8}]
Range[0, 20]! CoefficientList[Series[x^3/3 Exp[-x]/(1-x), {x, 0, 20}], x]

Crossrefs

Cf. A000387.

Sequence in context: A211880 A365862 A209868 * A189772 A217311 A266167

Adjacent sequences: A182658 A182659 A182660 * A182662 A182663 A182664

Keyword

nonn

Author

Geoffrey Critzer, Feb 01 2011

Status

approved