OFFSET
9,2
COMMENTS
Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 9.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 9..300
Wikipedia, Involution (mathematics)
Wikipedia, Young tableau
MAPLE
b:= proc(n) b(n):= `if`(n<2, 1, b(n-1) +(n-1)*b(n-2)) end:
g:= proc(n) option remember; `if`(n<4, [1, 1, 2, 4][n+1],
((40*n^3+1084*n^2+8684*n+18480)*g(n-1) +16*(n-1)
*(5*n^3+107*n^2+610*n+600)*g(n-2) -1024*(n-1)*(n-2)
*(n+6)*g(n-3) -1024*(n-1)*(n-2)*(n-3)*(n+4)*g(n-4))/
((n+7)*(n+12)*(n+15)*(n+16)))
end:
a:= n-> b(n) -g(n):
seq(a(n), n=9..30);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 24 2012
STATUS
approved