A145844 Number of permutations of length 2n which are invariant under the reverse-complement map and have no decreasing subsequences of length 5.

1, 2, 8, 46, 332, 2784, 25888, 259382, 2749244, 30449416, 349379648, 4127103776, 49954287424, 617299996928, 7765434294912, 99214734136966, 1285011754097372, 16845342401817048, 223216584359771296, 2986529546579794040, 40308007404730514096, 548337251596355725312

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = sum(j=0, n, A000108(j)*A000108(n-j)*C(n, j)^2 ) where A000108(n) = Catalan(n)= (2n)!/(n!(n+1)!) and C(n, j)=n!/(k!(n-j)!).

Recurrence: (n+1)^2*(n+2)*(3*n-1)*a(n) = 2*(30*n^4 + 11*n^3 - 20*n^2 - 3*n + 6)*a(n-1) - 64*(n-1)^3*(3*n+2)*a(n-2). - Vaclav Kotesovec, Feb 18 2015

a(n) ~ 2^(4*n+3) / (Pi^(3/2) * n^(7/2)). - Vaclav Kotesovec, Feb 18 2015

Example

a(4) = 1*1*14 + 16*1*5 + 36*2*2 + 16*5*1 + 1*14*1 = 332.

Mathematica

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

Crossrefs

Sequence in context: A276358 A337060 A141117 * A005840 A161881 A219358

Adjacent sequences: A145841 A145842 A145843 * A145845 A145846 A145847

Keyword

nonn

Author

Eric S. Egge, Oct 21 2008

Extensions

More terms from Vaclav Kotesovec, Feb 18 2015

Status

approved