%I A007999
%S A007999 1,1,2,3,8,19,64,213,880,3717,18288,92935,531440,3147495,20525168,
%T A007999 138638825,1015694832,7700244745,62623847536,526317901451,4705365925872,
%U A007999 43407723925499,423149546210416,4250149857500861,44868038386273776
%N A007999 a(n)=number of permutations w of 1,2,...,n such that w and w^{-1} are 
               alternating.
%D A007999 Foulkes, H. O.; Tangent and secant numbers and representations of symmetric 
               groups. Discrete Math. 15 (1976), no. 4, 311-324.
%D A007999 R. P. Stanley, Alternating permutations and symmetric functions, in preparation.
%H A007999 R. P. Stanley, <a href="http://arxiv.org/abs/math/0603520">Alternating 
               permutations and symmetric functions</a> [From Joel Brewster Lewis 
               (jblewis(AT)post.harvard.edu), May 21 2009]
%F A007999 sum_{n=0..infinity} a(n)x^n = sum_{k=0..infinity} E_{2k+1}^2 u^{2k+1}/
               (2k+1)! + (1-x^2)^{-1/2} sum_{k=0..infinity} E_{2k}^2 u^{2k}/(2k)!, 
               where E_j is an Euler number and u = (1/2)log((1+x)/(1-x)). - R. 
               P. Stanley (rstan(AT)math.mit.edu), Jan 21 2006
%Y A007999 Sequence in context: A148042 A077269 A148043 this_sequence A006609 A005663 
               A112834
%Y A007999 Adjacent sequences: A007996 A007997 A007998 this_sequence A008000 A008001 
               A008002
%K A007999 nonn
%O A007999 0,3
%A A007999 poirier(AT)lacim.uqam.ca, Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A007999 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), May 15 2007