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
Keywords
Examples
a(4) = 1*1*14 + 16*1*5 + 36*2*2 + 16*5*1 + 1*14*1 = 332.
Programs
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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}]
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
Extensions
More terms from Vaclav Kotesovec, Feb 18 2015