OFFSET
4,2
COMMENTS
Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 4. a(4)=1: 1234; a(5)=5: 12345, 12354, 12435, 13245, 21345.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 4..800
Wikipedia, Involution (mathematics)
Wikipedia, Young tableau
MAPLE
a:= proc(n) option remember;
`if`(n<5, [0$4, 1][n+1], ((-5-7*n+3*n^2)*a(n-1)
+(n-1)*(n^2-n-11)*a(n-2) -2*n*(n-1)*(n-2)*a(n-3)
-3*(n-1)*(n-2)*(n-3)*a(n-4))/((n+2)*(n-4)))
end:
seq(a(n), n=4..30);
MATHEMATICA
a[n_] := a[n] = If[n<5, {0, 0, 0, 0, 1}[[n+1]], ((-5-7n+3n^2)a[n-1] + (n-1)(n^2-n-11)a[n-2] - 2n(n-1)(n-2)a[n-3] - 3(n-1)(n-2)(n-3)a[n-4])/ ((n+2)(n-4))];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, Aug 23 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 24 2012
STATUS
approved