OFFSET
5,2
COMMENTS
Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 5. a(5)=1: 12345; a(6)=6: 123456, 123465, 123546, 124356, 132456, 213456.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 5..800
Wikipedia, Involution (mathematics)
Wikipedia, Young tableau
MAPLE
a:= proc(n) option remember; `if`(n<13,
[0$5, 1, 6, 36, 176, 856, 3952, 18272, 83524][n+1],
((n^4-2*n^3-179*n^2+256*n+804) *a(n-1)
+(n-1)*(n^4+6*n^3-295*n^2+1108*n+100) *a(n-2)
-4*(n-1)*(n-2)*(6*n^2-83*n+67) *a(n-3)
-16*(n-11)*(n-1)*(n-3)*(n-2)^2 *a(n-4))/
((n-12)*(n-5)*(n+4)*(n+3)))
end:
seq(a(n), n=5..30);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 24 2012
STATUS
approved