A368567 Number of Young tableaux of shape [n, floor(n/2)].

1, 1, 2, 3, 9, 14, 48, 75, 275, 429, 1638, 2548, 9996, 15504, 62016, 95931, 389367, 600875, 2466750, 3798795, 15737865, 24192090, 100975680, 154969620, 650872404, 997490844, 4211628008, 6446369400, 27341497800, 41802112192, 177996090624, 271861216539, 1161588834303, 1772528290407, 7596549816030, 11582393855305

Offset: 0

Author

Joerg Arndt, Dec 30 2023

Keywords

• nonn

Comments

Seemingly also the number of Catalan words of length n with at least ceiling(n/2) zeros. - Sela Fried, Jun 01 2025

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2417
• Joerg Arndt, The a(6)=48 Young tableaux of shape [6,3] and a(7)=75 Young tableaux of shape [7,3].

Crossrefs

Cf. A174687 (shape [2*n, n]), A026004 (shape [2*n+1, n]).

Programs

Maple

a:= proc(n) option remember; `if`(n<3, [1$2, 2][n+1],
      (4*n*(3027*n^2-10201*n+4134)*a(n-1)+6*(729*n^3-6201*n^2+9177*n-4921)*
      a(n-2)-3*(3*n-7)*(3027*n+1907)*(3*n-8)*a(n-3))/(8*(n+1)*n*(81*n-689)))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Jun 01 2025

Formula

a(2*n) = A174687(n/2), a(2*n+1) = A026004(n).