A214824 Number of solid standard Young tableaux of shape [[(2)^n],[2]].

2, 16, 91, 456, 2145, 9724, 43043, 187408, 806208, 3436720, 14545982, 61214960, 256411935, 1069854660, 4449173475, 18450500640, 76326664260, 315077780160, 1298203997610, 5340028714800, 21932944632690, 89963953083576, 368565304248846, 1508283816983776

Offset: 1

Author

Alois P. Heinz, Jul 28 2012

Keywords

• nonn

Comments

a(n) is odd if and only if n = 3 or n in { 2^k-3, 2^k-1 : k = 3,4,5, ... }.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012.
• G. Kreweras, Sur les extensions lineaires d'une famille particuliere d'ordres partiels, Discrete Math., 27 (1979), 279-295.
• G. Kreweras, Sur les extensions linéaires d'une famille particulière d'ordres partiels, Discrete Math., 27 (1979), 279-295. (Annotated scanned copy)
• Wikipedia, Young tableau

Crossrefs

Row n=2 of A214722 and of A259101.

Programs

Maple

a:= proc(n) option remember; `if`(n=1, 2,
      (4+(18+(22+4*n)*n)*n)*n*a(n-1)/(6+(-13+(1+(5+n)*n)*n)*n))
    end:
seq(a(n), n=1..30);

Mathematica

a[1] = 2; a[n_] := a[n] = (4 + (18 + (22 + 4*n)*n)*n)*n*a[n - 1]/(6 + (-13 + (1 + (5 + n)*n)*n)*n); Array[a, 30] (* Jean-François Alcover, Nov 08 2017, translated from Maple *)

Formula

a(n) = 2*(2*n+1)*(n^2+5*n+2)*n/((n-1)*(n+3)*(n^2+3*n-2))*a(n-1); a(1) = 2.