Search: id:A013989
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%I A013989
%S A013989 1,2,6,16,50,156,532,1856,6876,26200,104456,428352,1821976,
%T A013989 7959056,35857200,165592576,785514512,3812387616,18948962656,
%U A013989 96194028800,498931946016,2638959243712,14234346694976
%N A013989 a(n) = (n+1)( a(n-1)/n + a(n-2) ).
%C A013989 Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 28 2009: 
               (Start)
%C A013989 a(n) is also the number of fixed points in all involutions (= self-inverse 
               permutations) of {1,2,...,n+1}. Example: a(2)=6 because the involutions 
               of {1,2,3} are 1'2'3', 1'32, 32'1, and 213', containing 6 fixed points 
               (marked).
%C A013989 (End)
%C A013989 a(n) is also the number of adjacent transpositions in all involutions 
               (= self inverse permutations) of {1,2,...,n+2}. Example: a(2)=6 because 
               the involutions of {1,2,3,4} are 1234, 124*3, 13*24, 1432, 2*134, 
               2*14*3, 3214, 3412, 4231, and 43*21, containing 6 adjacent transpositions 
               (marked with *). [From Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Jun 08 2009]
%D A013989 rec.puzzles Dec 10 1995
%F A013989 E.g.f: x*exp(x*(x/2+1)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 28 2005
%p A013989 A013989 := proc(n) option remember; if n <=1 then n+1; else (n+1)*(A013989(n-1)/
               n+A013989(n-2)); fi; end;
%Y A013989 a(n) = A000085(n) * (n+1).
%Y A013989 Cf. A000085.
%Y A013989 Sequence in context: A052814 A151445 A000136 this_sequence A002841 A136509 
               A100664
%Y A013989 Adjacent sequences: A013986 A013987 A013988 this_sequence A013990 A013991 
               A013992
%K A013989 nonn,easy
%O A013989 0,2
%A A013989 N. J. A. Sloane (njas(AT)research.att.com), Dan Hoey (Hoey(AT)AIC.NRL.Navy.Mil)

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