A145847 Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequences of length 6.

1, 2, 6, 19, 67, 246, 947, 3746, 15213, 62950, 264920, 1129965, 4877215, 21262918, 93522756, 414532163, 1850047621, 8307290058, 37507875950, 170191051327, 775719275151, 3550191976022, 16309030657001, 75179696666964, 347658070586857, 1612424809368446

Offset: 0

Author

Eric S. Egge, Oct 21 2008

Keywords

• nonn

Links

• Nachum Dershowitz, Touchard's Drunkard, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.

Crossrefs

Cf. A001006, A001405.

Programs

Mathematica

Table[Sum[ Binomial[n, j]*Binomial[n - j, Floor[(n - j)/2]]* Sum[Binomial[j, 2*i]*Binomial[2*i, i]/(i + 1), {i, 0, Floor[j/2]}], {j, 0, n}], {n, 0, 20}]

Formula

a(n) = Sum_{j=0..n} binomial(n,j)*A001006(j)*A001405(n-j).

Recurrence: (n+2)*(n+3)*(8*n+7)*a(n) = 3*(8*n^3 + 39*n^2 + 51*n + 22)*a(n-1) + (n-1)*(104*n^2 + 155*n - 30)*a(n-2) - 15*(n-2)*(n-1)*(8*n+15)*a(n-3). - Vaclav Kotesovec, Feb 18 2015

a(n) ~ 5^(n+2) / (2*Pi*n^2). - Vaclav Kotesovec, Feb 18 2015

Extensions

More terms from Vaclav Kotesovec, Feb 18 2015