A318289 Number of standard Young tableaux of 2n cells and height >= n.

1, 2, 9, 56, 441, 3952, 40161, 442248, 5288933, 67100072, 904408398, 12777826272, 189324035423, 2917525618256, 46754429476800, 774965979970096, 13279872426589125, 234395323126241080, 4258775222885983350, 79442662095373693728, 1520453631213137081776

Offset: 0

Author

Alois P. Heinz, Nov 04 2018

Keywords

• nonn

Comments

Also number of self-inverse permutations of [2n] with longest increasing subsequence of length >= n.

Links

• Wikipedia, Involution (mathematics)
• Wikipedia, Young tableau

Crossrefs

Cf. A182222.

Programs

Mathematica

h[l_] := Module[{n = Length[l]}, Total[l]!/Product[Product[1+l[[i]]-j+Sum[ If[l[[k]] >= j, 1, 0], {k, i+1, n}], {j, 1, l[[i]]}], {i, 1, n}]];
g[n_, i_, l_] := g[n, i, l] = If[n == 0, h[l], If[i < 1, 0, If[i == 1, h[Join[l, Array[1&, n]]], g[n, i-1, l] + If[i > n, 0, g[n-i, i, Append[l, i]]]]]];
t[n_, k_] := g[n, n, {}] - If[k == 0, 0, g[n, k-1, {}]];
a[n_] := a[n] = t[2n, n];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 20}] (* Jean-François Alcover, Sep 08 2021, after Alois P. Heinz in A182222 *)

Formula

a(n) = A182222(2n,n).