A218267 Number of standard Young tableaux of n cells and height >= 7.

1, 8, 64, 400, 2465, 14092, 80016, 442248, 2442351, 13375366, 73477622, 403703404, 2230591660, 12380801756, 69225756076, 389806286920, 2213844625658, 12681996193252, 73339826141716, 428242854338216, 2526129602115517, 15056977593085444, 90712249806247400

Offset: 7

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 >= 7. a(7)=1: 1234567; a(8)=8: 12345678, 12345687, 12345768, 12346578, 12354678, 12435678, 13245678, 21345678.

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..300
• Wikipedia, Involution (mathematics)
• Wikipedia, Young tableau

Crossrefs

Column k=7 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], ((20*n^2+184*n+336)*g(n-1)
       +4*(n-1)*(10*n^2+58*n+33)*g(n-2) -144*(n-1)*(n-2)*g(n-3)
       -144*(n-1)*(n-2)*(n-3)*g(n-4)) / ((n+5)*(n+8)*(n+9)))
    end:
a:= n-> b(n) -g(n):
seq(a(n), n=7..30);

Formula

a(n) = A000085(n) - A007579(n) = A182172(n,n) - A182172(n,6).