%I A145844
%S A145844 1,2,8,46,332,2784,25888,259382,2749244,30449416,349379648
%N A145844 Number of permutations of length 2n which are invariant under the reverse-complement 
               map and have no decreasing subsequences of length 5.
%F A145844 a(n) = sum(j=0, n, A000108(j)*A000108(n-j)*C(n, j)^2 ) where
%F A145844 A000108(n)=Catalan(n)=(2n)!/(n!(n+1)!) and C(n, j)=n!/(k!(n-j)!)
%e A145844 a(4) = 1*1*14 + 16*1*5 + 36*2*2 + 16*5*1 + 1*14*1 = 332
%t A145844 Table[Sum[ Binomial[n, j]^2*Binomial[2*j, j]* Binomial[2*(n - j), n - 
               j]/((n - j + 1)*(j + 1)), {j, 0, n}], {n, 0, 20}]
%Y A145844 Sequence in context: A119501 A006664 A141117 this_sequence A005840 A161881 
               A088791
%Y A145844 Adjacent sequences: A145841 A145842 A145843 this_sequence A145845 A145846 
               A145847
%K A145844 nonn
%O A145844 0,2
%A A145844 Eric Egge (eegge(AT)carleton.edu), Oct 21 2008