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A237928 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.

%I A237928 #10 Apr 26 2016 12:43:54
%S A237928 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 A237928 1,3759,2800,1239,420,70,21,0,1,30310,22980,10570,2884,735,112,28,0,1,
%U A237928 272817,202797,87534,24780,6489,1134,168,36,0,1
%N A237928 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 A237928 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 A237928 1,
%e A237928 1,    1,
%e A237928 2,    1,    1,
%e A237928 3,    3,    0,    1,
%e A237928 18,   14,   9,    0,   1,
%e A237928 95,   75,   35,   10,  0,  1,
%e A237928 540,  369,  135,  55,  15, 0,  1,
%e A237928 3759, 2800, 1239, 420, 70, 21, 0, 1
%e A237928 T(3,0)=3 because we have: (1)(2)(3);(1,2,3);(2,1,3)
%t A237928 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 A237928 nonn,tabl
%O A237928 0,4
%A A237928 _Geoffrey Critzer_, Feb 15 2014