A218269 Number of standard Young tableaux of n cells and height >= 9.

1, 10, 100, 760, 5656, 38416, 257376, 1660416, 10640692, 67100072, 422374352, 2643349180, 16566306380, 103786892840, 652502735152, 4113403313016, 26057914447911, 165824119892086, 1061381766546172, 6832087071296824, 44260892997918920, 288574772339715376

Offset: 9

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 >= 9.

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..300
• Wikipedia, Involution (mathematics)
• Wikipedia, Young tableau

Crossrefs

Column k=9 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<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);

Formula

a(n) = A000085(n) - A007580(n) = A182172(n,n) - A182172(n,8).