A218265 Number of standard Young tableaux of n cells and height >= 5.

1, 6, 36, 176, 856, 3952, 18272, 83524, 384463, 1777010, 8304636, 39254076, 188160268, 915651672, 4527595824, 22771294440, 116496899100, 606656445480, 3214574890480, 17337658462800, 95128543350576, 530998366724576, 3013524116661952, 17385349086129304

Offset: 5

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 >= 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

Crossrefs

Column k=5 of A182222.

Programs

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);

Formula

a(n) = A000085(n) - A005817(n) = A182172(n,n) - A182172(n,4).