|
|
A145846
|
|
Number of permutations of length 2n which are invariant under the reverse-complement map and have no decreasing subsequences of length 6.
|
|
0
|
|
|
1, 2, 8, 47, 357, 3270, 34515, 406460, 5215829, 71677058, 1041363040, 15841778155, 250494079945, 4093630537014, 68830515423498, 1186424966652225, 20902566718237725, 375485138838707850, 6863181435514906992, 127420716337372828539, 2399321143670605041105
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
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
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|