A212650 Number of permutations of n elements with at least one fixed point and at least one 2-cycle (transposition).

0, 0, 0, 3, 6, 25, 180, 1281, 10010, 90063, 902790, 9929755, 119134224, 1548768585, 21683033372, 325245031125, 5203916869710, 88466595897631, 1592398778725710, 30255576613653483, 605111531456405960, 12707342164389159945, 279561527629906821684

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

E.g.f.: (exp(x)-1)*(exp(x^2/2)-1)*exp(-x - x^2/2)/(1-x).

a(n) ~ n! * (exp(1)-1)*(exp(1/2)-1)*exp(-3/2) = n! * 0.248720059264354... - Vaclav Kotesovec, Aug 07 2013

Example

a(3) = 3: 132, 213, 321.
a(4) = 6: 1243, 1324, 1432, 2134, 3214, 4231.

Mathematica

nn=22; Range[0, nn]!CoefficientList[Series[(Exp[x]-1)(Exp[x^2/2]-1)Exp[-x-x^2/2]/(1-x), {x, 0, nn}], x]

Crossrefs

Cf. A002467.

Sequence in context: A350752 A355967 A074432 * A297572 A137089 A197470

Adjacent sequences: A212647 A212648 A212649 * A212651 A212652 A212653

Keyword

nonn

Author

Geoffrey Critzer, Feb 14 2013

Status

approved