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%I #24 Jul 14 2023 15:18:25
%S 1,2,3,5,10,22,49,107,228,476,979,1993,4030,8114,16293,32663,65416,
%T 130936,261991,524117,1048386,2096942,4194073,8388355,16776940,
%U 33554132,67108539,134217377,268435078,536870506,1073741389,2147483183
%N a(n) = 2^n - n*(n-1)/2.
%C a(n) is the number of subsets of {1,2,...,n} that do not have a cardinality of 2. - _Geoffrey Critzer_, Feb 25 2012
%H Vincenzo Librandi, <a href="/A014844/b014844.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5, -9, 7, -2).
%F E.g.f.: exp(x)*(exp(x)-x^2/2!). - _Geoffrey Critzer_, Feb 25 2012
%F G.f.: (1-3*x+2*x^2+x^3)/((1-x)^3*(1-2*x)). - _Colin Barker_, Apr 01 2012
%t nn = 20;Range[0, nn]! CoefficientList[Series[Exp[x] (Exp[x] - x^2/2!), {x, 0, nn}], x] (* _Geoffrey Critzer_, Feb 25 2012 *)
%t CoefficientList[Series[(1-3*x+2*x^2+x^3)/((1-x)^3*(1-2*x)),{x,0,33}],x] (* _Vincenzo Librandi_, Apr 18 2012 *)
%o (Magma) [2^n - n*(n-1)/2: n in [0..40]]; // _Vincenzo Librandi_, Apr 18 2012
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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