%I A003221 M0922
%S A003221 1,0,0,2,3,24,130,930,7413,66752,667476,7342290,88107415,1145396472,
%T A003221 16035550518,240533257874,3848532125865,65425046139840,1177650830516968,
%U A003221 22375365779822562,447507315596451051,9397653627525472280,206748379805560389930
%N A003221 Number of even permutations of length n with no fixed points.
%D A003221 Ali, Bashir and Umar, A., "Some combinatorial properties of the alternating 
               group". Southeast Asian Bulletin Math. 32 (2008), 823-830. [From 
               A. Umar (aumarh(AT)squ.edu.om), Oct 09 2008]
%D A003221 Problem E2354, Amer. Math. Monthly, 79 (1972), 394.
%D A003221 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%F A003221 Contribution from A. Umar (aumarh(AT)squ.edu.om), Oct 09 2008: (Start)
%F A003221 a(n)=(n!/2)sum(i=0,n-2,((-1)^i)/i!)+((-1)^(n-1))(n-1),(n>1),a(0)=1, a(1)=0;
%F A003221 a(n)=(n-1)(a(n-1)+a(n-2)))+((-1)^(n-1))(n-1), a(0)=1, a(1)=0;
%F A003221 a(n)=na(n-1)+((-1)^(n-1))(n-2)(n+1)/2, a(0)=1.
%F A003221 Egf. (1-x^2/2)e^(-x)/(1-x). (End)
%p A003221 a(n)=(A000166(n)-(-1)^n*(n-1))/2.
%Y A003221 Cf. A000166.
%Y A003221 Sequence in context: A009231 A012304 A047157 this_sequence A013312 A013318 
               A048674
%Y A003221 Adjacent sequences: A003218 A003219 A003220 this_sequence A003222 A003223 
               A003224
%K A003221 nonn,easy,nice
%O A003221 0,4
%A A003221 N. J. A. Sloane (njas(AT)research.att.com).