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A145847
Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequences of length 6.
11
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
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
Sequence in context: A150095 A150096 A150097 * A150098 A184018 A148470
KEYWORD
nonn
AUTHOR
Eric S. Egge, Oct 21 2008
EXTENSIONS
More terms from Vaclav Kotesovec, Feb 18 2015
STATUS
approved