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

0,2

Links

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

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

Formula

a(n) = Sum_{j=0..n} C(n,j)*A001006(j)*A001405(n-j), where C(n,j) = n!/(j!(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

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}]

Crossrefs

Cf. A001006, A001405.

Sequence in context: A150095 A150096 A150097 * A150098 A184018 A148470

Adjacent sequences: A145844 A145845 A145846 * A145848 A145849 A145850

Keyword

nonn

Author

Eric S. Egge, Oct 21 2008

Extensions

More terms from Vaclav Kotesovec, Feb 18 2015

Status

approved