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

%I A214824 #29 Nov 08 2017 08:57:58
%S A214824 2,16,91,456,2145,9724,43043,187408,806208,3436720,14545982,61214960,
%T A214824 256411935,1069854660,4449173475,18450500640,76326664260,315077780160,
%U A214824 1298203997610,5340028714800,21932944632690,89963953083576,368565304248846,1508283816983776
%N A214824 Number of solid standard Young tableaux of shape [[(2)^n],[2]].
%C A214824 a(n) is odd if and only if n = 3 or n in { 2^k-3, 2^k-1 : k = 3,4,5, ... }.
%H A214824 Alois P. Heinz, <a href="/A214824/b214824.txt">Table of n, a(n) for n = 1..1000</a>
%H A214824 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 A214824 G. Kreweras, <a href="http://dx.doi.org/10.1016/0012-365X(79)90163-8">Sur les extensions lineaires d'une famille particuliere d'ordres partiels</a>, Discrete Math., 27 (1979), 279-295.
%H A214824 G. Kreweras, <a href="/A006330/a006330_1.pdf">Sur les extensions linéaires d'une famille particulière d'ordres partiels</a>, Discrete Math., 27 (1979), 279-295. (Annotated scanned copy)
%H A214824 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A214824 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.
%p A214824 a:= proc(n) option remember; `if`(n=1, 2,
%p A214824       (4+(18+(22+4*n)*n)*n)*n*a(n-1)/(6+(-13+(1+(5+n)*n)*n)*n))
%p A214824     end:
%p A214824 seq(a(n), n=1..30);
%t A214824 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 *)
%Y A214824 Row n=2 of A214722 and of A259101.
%K A214824 nonn
%O A214824 1,1
%A A214824 _Alois P. Heinz_, Jul 28 2012