A218266 Number of standard Young tableaux of n cells and height >= 6.

1, 7, 49, 273, 1506, 7788, 40161, 202917, 1028170, 5190328, 26375635, 134565795, 692890250, 3596739368, 18877483060, 100131220940, 537718999715, 2922918175965, 16100254700137, 89857257410905, 508473405642250, 2916903963927300, 16969580464205400

Offset: 6

Author

Alois P. Heinz, Oct 24 2012

Keywords

• nonn

Comments

Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 6. a(6)=1: 123456; a(7)=7: 1234567, 1234576, 1234657, 1235467, 1243567, 1324567, 2134567.

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..300
• Wikipedia, Involution (mathematics)
• Wikipedia, Young tableau

Crossrefs

Column k=6 of A182222.

Programs

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<3, [1, 1, 2][n+1],
      ((3*n^2+17*n+15)*g(n-1) +(n-1)*(13*n+9)*g(n-2)
       -15*(n-1)*(n-2)*g(n-3)) / ((n+4)*(n+6)))
    end:
a:= n-> b(n) -g(n):
seq(a(n), n=6..30);

Formula

a(n) = A000085(n) - A049401(n) = A182172(n,n) - A182172(n,5).