A145867 Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequence of length 7.

1, 2, 6, 20, 74, 292, 1214, 5252, 23468, 107672, 505048, 2413776, 11723188, 57737032, 287853518, 1450697572, 7381645844, 37884748712, 195947389208, 1020610698832, 5349968198328, 28208066576176, 149526042974008, 796520870628752, 4262367319460848

Offset: 0

Author

Eric S. Egge, Oct 22 2008

Keywords

• nonn

Crossrefs

Cf. A001006.

Programs

Mathematica

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}]

Formula

a(n) = sum(j,0,n, C(n,j)*A001006(j)*A001006(n-j)), where C(n,j) = n!/(j!(n-j)!).

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

a(n) ~ 9 * 6^(n+1) / (Pi * n^3). - Vaclav Kotesovec, Feb 18 2015

E.g.f.: exp(2*x)*BesselI(1,2*x)^2/x^2. - Ilya Gutkovskiy, Sep 21 2017

Extensions

More terms from Alois P. Heinz, Feb 18 2015