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%I #10 Apr 26 2016 12:43:54
%S 1,1,1,2,1,1,3,3,0,1,18,14,9,0,1,95,75,35,10,0,1,540,369,135,55,15,0,
%T 1,3759,2800,1239,420,70,21,0,1,30310,22980,10570,2884,735,112,28,0,1,
%U 272817,202797,87534,24780,6489,1134,168,36,0,1
%N Triangular array read by rows. T(n,k) is the number of n-permutations with k cycles of length one or k cycles of length two, n>=0,0<=k<=n.
%F E.g.f.: A(x,y) + B(x,y) - C(x,y) where A(x,y) is e.g.f. for A008290, B(x,y) is e.g.f. for A114320, and C(x,y) = exp(-x - x^2/2)/(1-x)*Sum_{n>=0}y^n*x^(3n)/(2^n*n!^2).
%e 1,
%e 1, 1,
%e 2, 1, 1,
%e 3, 3, 0, 1,
%e 18, 14, 9, 0, 1,
%e 95, 75, 35, 10, 0, 1,
%e 540, 369, 135, 55, 15, 0, 1,
%e 3759, 2800, 1239, 420, 70, 21, 0, 1
%e T(3,0)=3 because we have: (1)(2)(3);(1,2,3);(2,1,3)
%t nn=10;c=Sum[y^n x^(3n)/(2^n*n!^2),{n,0,nn}];Table[Take[(Range[0,nn]!CoefficientList[Series[Exp[y x]Exp[-x]/(1-x)+Exp[y x^2/2]Exp[-x^2/2]/(1-x)-c Exp[-x-x^2/2!]/(1-x),{x,0,nn}],{x,y}])[[n]],n],{n,1,nn}]//Grid
%K nonn,tabl
%O 0,4
%A _Geoffrey Critzer_, Feb 15 2014
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