A145846 Number of permutations of length 2n which are invariant under the reverse-complement map and have no decreasing subsequences of length 6.

1, 2, 8, 47, 357, 3270, 34515, 406460, 5215829, 71677058, 1041363040, 15841778155, 250494079945, 4093630537014, 68830515423498, 1186424966652225, 20902566718237725, 375485138838707850, 6863181435514906992, 127420716337372828539, 2399321143670605041105

Offset: 0

Author

Eric S. Egge, Oct 21 2008

Keywords

• nonn

Programs

Mathematica

Table[Sum[ Binomial[n, j]^2*((1/(n - j + 1))* Binomial[2*(n - j), n - j]/((j + 1)^2*(j + 2)))* Sum[Binomial[2*i, i]*Binomial[j + 1, i + 1]* Binomial[j + 2, i + 1], {i, 0, j}], {j, 0, n}], {n, 0, 20}]

Formula

a(n) = sum(j, 0, n, C(n,j)^2 * A000108(n-j) * A005802(j)), where C(n,j) = n!/(j!(n-j)!).

Recurrence: (n+2)^2*(n+3)^2*(64*n^3 + 96*n^2 - 36*n - 79)*a(n) = (2240*n^7 + 13664*n^6 + 26068*n^5 + 7303*n^4 - 27638*n^3 - 20581*n^2 + 5964*n + 5940)*a(n-1) - (n-1)^2*(16576*n^5 + 61344*n^4 + 25556*n^3 - 84501*n^2 - 46860*n - 15300)*a(n-2) + 225*(n-2)^2*(n-1)^2*(64*n^3 + 288*n^2 + 348*n + 45)*a(n-3). - Vaclav Kotesovec, Feb 18 2015

a(n) ~ 5^(2*n+13/2) / (128 * Pi^2 * n^6). - Vaclav Kotesovec, Feb 18 2015

Extensions

More terms from Vaclav Kotesovec, Feb 18 2015