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A145867
Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequence of length 7.
11
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
OFFSET
0,2
FORMULA
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
a(n) ~ 9 * 6^(n+1) / (Pi * n^3). - Vaclav Kotesovec, Feb 18 2015
E.g.f.: exp(2*x)*BesselI(1,2*x)^2/x^2. - Ilya Gutkovskiy, Sep 21 2017
MATHEMATICA
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}]
CROSSREFS
Cf. A001006.
Sequence in context: A150156 A150157 A371712 * A188144 A245734 A150158
KEYWORD
nonn
AUTHOR
Eric S. Egge, Oct 22 2008
EXTENSIONS
More terms from Alois P. Heinz, Feb 18 2015
STATUS
approved