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A145867
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Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequence of length 7.
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11
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1, 2, 6, 20, 74, 292, 1214, 5252, 23468, 107672, 505048, 2413776, 11723188, 57737032, 287853518, 1450697572, 7381645844, 37884748712, 195947389208, 1020610698832, 5349968198328, 28208066576176, 149526042974008, 796520870628752, 4262367319460848
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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)*A001006(n-j)), where C(n,j) = n!/(j!(n-j)!).
Recurrence: (n+2)*(n+4)*a(n) = 6*(n^2 + 3*n + 1)*a(n-1) + 4*(n-1)*(n+1)*a(n-2) - 24*(n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Feb 18 2015
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MATHEMATICA
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Array[Cat, 21, 0]; For[i = 0, i < 21, ++i, Cat[i] = (1/(i + 1))*Binomial[2*i, i]]; Array[Mot, 21, 0]; For[i = 0, i < 21, ++i, Mot[i] = Sum[Binomial[i, 2*j]*Cat[j], {j, 0, Floor[i/2]}]]; Table[Sum[Binomial[n, j]*Mot[j]*Mot[n - j], {j, 0, n}], {n, 0, 15}]
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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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