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A145847
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Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequences of length 6.
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11
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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