A145868 Number of involutions of length 2n+1 which are invariant under the reverse-complement map and have no decreasing subsequences of length 7.

1, 2, 6, 19, 68, 255, 1020, 4221, 18186, 80304, 364476, 1684782, 7944156, 37988379, 184406508, 905147815, 4495346570, 22527055980, 113957354940, 580759868910, 2982724210440, 15414453711930, 80177422383240, 419249099692710, 2204316120027420, 11642676960438000

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = sum(j,0,n, C(n,j)*C(n-j,floor((n-j)/2))*A000108(floor((j+1)/2)) * A000108(ceiling((j+1)/2))), where C(n,j) = n!/(j!(n-j)!) and A000108(n) = Catalan(n).

Recurrence: (n+3)*(n+4)*(n+5)*(2*n+1)*(2*n+3)*a(n) = 8*(2*n+1)*(5*n^3 + 33*n^2 + 67*n + 45)*a(n-1) + 4*(n-1)*(40*n^4 + 216*n^3 + 326*n^2 + 144*n + 45)*a(n-2) - 288*(n-2)*(n-1)*(n+1)*(2*n+5)*a(n-3) - 144*(n-3)*(n-2)*(n-1)*(2*n+3)*(2*n+5)*a(n-4). - Vaclav Kotesovec, Feb 18 2015

a(n) ~ 6^(n+7/2) / (2 * Pi^(3/2) * n^(7/2)). - Vaclav Kotesovec, Feb 18 2015

Mathematica

Array[Cat, 21, 0]; For[i = 0, i < 21, ++i, Cat[i] = (1/(i + 1))*Binomial[2*i, i]]; Table[Sum[ Binomial[n, j]*Binomial[n - j, Floor[(n - j)/2]]* Cat[Floor[(j + 1)/2]]*Cat[Ceiling[(j + 1)/2]], {j, 0, n}], {n, 0, 15}]

Crossrefs

Sequence in context: A150102 A150103 A150104 * A376077 A058122 A150105

Adjacent sequences: A145865 A145866 A145867 * A145869 A145870 A145871

Keyword

nonn

Author

Eric S. Egge, Oct 22 2008

Extensions

More terms from Vaclav Kotesovec, Feb 18 2015

Status

approved