0,2

Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 28 2009: (Start)

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).

(End)

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]

rec.puzzles Dec 10 1995

E.g.f: x*exp(x*(x/2+1)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 28 2005

A013989 := proc(n) option remember; if n <=1 then n+1; else (n+1)*(A013989(n-1)/n+A013989(n-2)); fi; end;

a(n) = A000085(n) * (n+1).

Cf. A000085.

Sequence in context: A052814 A151445 A000136 this_sequence A002841 A136509 A100664

Adjacent sequences: A013986 A013987 A013988 this_sequence A013990 A013991 A013992

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com), Dan Hoey (Hoey(AT)AIC.NRL.Navy.Mil)