OFFSET
3,2
COMMENTS
Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 3. a(3)=1: 123; a(4)=4: 1234, 1243, 1324, 2134.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 3..800
Wikipedia, Involution (mathematics)
Wikipedia, Young tableau
FORMULA
Conjecture: (n-6)*(n-3)*(n+1)*a(n) +(-n^3+6*n^2+11*n-36)*a(n-1) -(n-1)*(n^3-4*n^2-21*n+76)*a(n-2) +2*(n-1)*(n-2)*(3*n-19)*a(n-3) +4*(n-5)*(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Jan 04 2017
MAPLE
b:= proc(n) b(n):= `if`(n<2, 1, b(n-1) +(n-1)*b(n-2)) end:
a:= n-> b(n) -binomial(n, iquo(n, 2)):
seq(a(n), n=3..30);
MATHEMATICA
b[n_] := b[n] = If[n<2, 1, b[n-1] + (n-1)*b[n-2]];
a[n_] := b[n] - Binomial[n, Quotient[n, 2]];
Table[a[n], {n, 3, 30}] (* Jean-François Alcover, Aug 23 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 24 2012
STATUS
approved