%I A086618
%S A086618 1,2,7,33,183,1118,7281,49626,349999,2535078,18758265,141254655,
%T A086618 1079364105,8350678170,65298467487,515349097713,4100346740511,
%U A086618 32858696386766,265001681344569
%N A086618 Main diagonal of square table A086617 of coefficients, T(n,k), of x^n*y^k 
               in f(x,y) that satisfies f(x,y) = 1/[(1-x)(1-y)] + xy*f(x,y)^2.
%C A086618 Contribution from Eric Egge (eegge(AT)carleton.edu), Oct 21 2008: (Start)
%C A086618 a(n) is the number of permutations of length 2n which are invariant
%C A086618 under the reverse-complement map and have no decreasing subsequences
%C A086618 of length 4. (End)
%F A086618 a(n) = sum(k=0, n, A000108(k)*C(n, k)^2 ) where A000108(n)=Catalan(n)=(2n)!/
               (n!(n+1)!) and C(n, k)=n!/(k!(n-k)!). (From Michael Somos)
%e A086618 a(5)= 1118 = 1*1^2 + 1*5^2 + 2*10^2 + 5*10^2 + 14*5^2 + 42*1^2.
%Y A086618 Cf. A086617 (table), A086615 (antidiagonal sums), A003046 (determinants).
%Y A086618 Cf. A000108.
%Y A086618 Sequence in context: A162257 A055724 A054727 this_sequence A162661 A104981 
               A058797
%Y A086618 Adjacent sequences: A086615 A086616 A086617 this_sequence A086619 A086620 
               A086621
%K A086618 nonn
%O A086618 0,2
%A A086618 Paul D. Hanna (pauldhanna(AT)juno.com), Jul 24 2003