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%I #17 Jan 26 2019 05:44:47
%S 1,2,6,19,67,246,947,3746,15213,62950,264920,1129965,4877215,21262918,
%T 93522756,414532163,1850047621,8307290058,37507875950,170191051327,
%U 775719275151,3550191976022,16309030657001,75179696666964,347658070586857,1612424809368446
%N Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequences of length 6.
%H Nachum Dershowitz, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Dershowitz/dersh3.html">Touchard’s Drunkard</a>, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.
%F a(n) = Sum_{j=0..n} C(n,j)*A001006(j)*A001405(n-j), where C(n,j) = n!/(j!(n-j)!).
%F 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
%F a(n) ~ 5^(n+2) / (2*Pi*n^2). - _Vaclav Kotesovec_, Feb 18 2015
%t 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}]
%Y Cf. A001006, A001405.
%K nonn
%O 0,2
%A _Eric S. Egge_, Oct 21 2008
%E More terms from _Vaclav Kotesovec_, Feb 18 2015
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