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

0,2

Links

Table of n, a(n) for 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

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}]

Crossrefs

Sequence in context: A298698 A354498 A135904 * A317366 A009566 A349588

Adjacent sequences: A145843 A145844 A145845 * A145847 A145848 A145849

Keyword

nonn

Author

Eric S. Egge, Oct 21 2008

Extensions

More terms from Vaclav Kotesovec, Feb 18 2015

Status

approved