%I A117513
%S A117513 1,2,12,136,2480,66336,2446528,118984832,7378078464,568142287360,
%T A117513 53189920492544,5949749335001088,783686338494312448,
%U A117513 120058889459865165824,21166245289132322242560
%N A117513 Number of ways of arranging 2n tokens in a row, with 2 copies of each 
               token from 1 through n, such that between every pair of tokens labeled 
               i (i=1..n-1) there is exactly one taken labeled i+1.
%C A117513 Contribution from Paul Barry (pbarry(AT)wit.ie), Oct 12 2009: (Start)
%C A117513 The aerated sequence is a(n)=(2^(n/2-1)+0^(n/2)/2)*((1+(-1)^n)/2)*n!*[x^n](1+x*tan(x/
               2)).
%C A117513 Multiples of the unsigned Genocchi numbers A110501: (1,1,3,17,155,...)*(1,
               2,4,8,16,...) (End)
%F A117513 G.f.: 1/(1-2x/(1-4x/(1-8x/(1-12x/(1-18x/(1-24x/(1-32x/(1-.../(1-2*floor((n+2)^2/
               4)*x/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), 
               Dec 03 2009]
%Y A117513 Cf. A002105, A117514, A117515.
%Y A117513 Sequence in context: A077696 A117271 A108996 this_sequence A119819 A093543 
               A091144
%Y A117513 Adjacent sequences: A117510 A117511 A117512 this_sequence A117514 A117515 
               A117516
%K A117513 nonn,new
%O A117513 1,2
%A A117513 Nan Zang (nzang(AT)cs.ucsd.edu), Apr 28 2006
%E A117513 More terms from Paul Barry (pbarry(AT)wit.ie), Oct 12 2009