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

Author

Geoffrey Critzer, Feb 14 2013

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A002467.

Programs

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]

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