cp's OEIS Frontend

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

%I A145846 #10 Feb 18 2015 18:09:17
%S A145846 1,2,8,47,357,3270,34515,406460,5215829,71677058,1041363040,
%T A145846 15841778155,250494079945,4093630537014,68830515423498,
%U A145846 1186424966652225,20902566718237725,375485138838707850,6863181435514906992,127420716337372828539,2399321143670605041105
%N A145846 Number of permutations of length 2n which are invariant under the reverse-complement map and have no decreasing subsequences of length 6.
%F A145846 a(n) = sum(j, 0, n, C(n,j)^2 * A000108(n-j) * A005802(j)), where C(n,j) = n!/(j!(n-j)!).
%F A145846 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
%F A145846 a(n) ~ 5^(2*n+13/2) / (128 * Pi^2 * n^6). - _Vaclav Kotesovec_, Feb 18 2015
%t A145846 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}]
%K A145846 nonn
%O A145846 0,2
%A A145846 _Eric S. Egge_, Oct 21 2008
%E A145846 More terms from _Vaclav Kotesovec_, Feb 18 2015