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A215220 Number of solid standard Young tableaux of shape [[n,n,n,n],[n]].

%I A215220 #15 Nov 08 2017 09:53:15
%S A215220 1,4,456,143164,75965484,55824699632,51274161733160,55418842406649988,
%T A215220 67819708829687672202,91539069926354814114556,
%U A215220 133752944758581353219955762,208673064320580765981337783096,343997162091593719562479905281938,594344377404793356460064021706935470
%N A215220 Number of solid standard Young tableaux of shape [[n,n,n,n],[n]].
%H A215220 Alois P. Heinz, <a href="/A215220/b215220.txt">Table of n, a(n) for n = 0..40</a>
%H A215220 S. B. Ekhad, D. Zeilberger, <a href="https://arxiv.org/abs/1202.6229">Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux</a>, arXiv:1202.6229v1 [math.CO], 2012
%H A215220 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%p A215220 b:= proc(w, x, y, z, u) option remember;
%p A215220      `if`({w, x, y, z, u}={0}, 1, `if`(w>x and w>u, b(w-1, x, y, z, u), 0)+
%p A215220      `if`(x>y, b(w, x-1, y, z, u), 0)+ `if`(y>z, b(w, x, y-1, z, u), 0)+
%p A215220      `if`(z>0, b(w, x, y, z-1, u), 0)+ `if`(u>0, b(w, x, y, z, u-1), 0))
%p A215220     end:
%p A215220 a:= n-> b(n$5):
%p A215220 seq(a(n), n=0..20);
%t A215220 b[w_, x_, y_, z_, u_] := b[w, x, y, z, u] =
%t A215220   If[Union@{w, x, y, z, u} == {0}, 1,
%t A215220   If[w > x && w > u, b[w - 1, x, y, z, u], 0] +
%t A215220   If[x > y, b[w, x - 1, y, z, u], 0] +
%t A215220   If[y > z, b[w, x, y - 1, z, u], 0] +
%t A215220   If[z > 0, b[w, x, y, z - 1, u], 0] +
%t A215220   If[u > 0, b[w, x, y, z, u - 1], 0]];
%t A215220 a[n_] :=  b[n, n, n, n, n];
%t A215220 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Nov 08 2017, translated from Maple *)
%Y A215220 Column k=4 of A214722.
%K A215220 nonn
%O A215220 0,2
%A A215220 _Alois P. Heinz_, Aug 06 2012