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%I #18 Aug 07 2013 16:51:31
%S 0,0,0,3,6,25,180,1281,10010,90063,902790,9929755,119134224,
%T 1548768585,21683033372,325245031125,5203916869710,88466595897631,
%U 1592398778725710,30255576613653483,605111531456405960,12707342164389159945,279561527629906821684
%N Number of permutations of n elements with at least one fixed point and at least one 2-cycle (transposition).
%H Alois P. Heinz, <a href="/A212650/b212650.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: (exp(x)-1)*(exp(x^2/2)-1)*exp(-x - x^2/2)/(1-x).
%F a(n) ~ n! * (exp(1)-1)*(exp(1/2)-1)*exp(-3/2) = n! * 0.248720059264354... - _Vaclav Kotesovec_, Aug 07 2013
%e a(3) = 3: 132, 213, 321.
%e a(4) = 6: 1243, 1324, 1432, 2134, 3214, 4231.
%t 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]
%Y Cf. A002467.
%K nonn
%O 0,4
%A _Geoffrey Critzer_, Feb 14 2013
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