|
%I #15 Sep 21 2017 19:54:50
%S 1,2,6,20,74,292,1214,5252,23468,107672,505048,2413776,11723188,
%T 57737032,287853518,1450697572,7381645844,37884748712,195947389208,
%U 1020610698832,5349968198328,28208066576176,149526042974008,796520870628752,4262367319460848
%N Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequence of length 7.
%F a(n) = sum(j,0,n, C(n,j)*A001006(j)*A001006(n-j)), where C(n,j) = n!/(j!(n-j)!).
%F Recurrence: (n+2)*(n+4)*a(n) = 6*(n^2 + 3*n + 1)*a(n-1) + 4*(n-1)*(n+1)*a(n-2) - 24*(n-2)*(n-1)*a(n-3). - _Vaclav Kotesovec_, Feb 18 2015
%F a(n) ~ 9 * 6^(n+1) / (Pi * n^3). - _Vaclav Kotesovec_, Feb 18 2015
%F E.g.f.: exp(2*x)*BesselI(1,2*x)^2/x^2. - _Ilya Gutkovskiy_, Sep 21 2017
%t Array[Cat, 21, 0]; For[i = 0, i < 21, ++i, Cat[i] = (1/(i + 1))*Binomial[2*i, i]]; Array[Mot, 21, 0]; For[i = 0, i < 21, ++i, Mot[i] = Sum[Binomial[i, 2*j]*Cat[j], {j, 0, Floor[i/2]}]]; Table[Sum[Binomial[n, j]*Mot[j]*Mot[n - j], {j, 0, n}], {n, 0, 15}]
%Y Cf. A001006.
%K nonn
%O 0,2
%A _Eric S. Egge_, Oct 22 2008
%E More terms from _Alois P. Heinz_, Feb 18 2015
|
