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A211505 Number of solid standard Young tableaux of shape [[(3)^n],[3]].

%I A211505 #41 Jul 19 2017 20:21:19
%S A211505 5,192,5471,143164,3636776,91442364,2293620329,57583680440,
%T A211505 1449149180310,36577522323264,926132803592304,23521922685452320,
%U A211505 599176262762762880,15305331537941936820,391972832520910172865,10062682947669846370800,258904473727824391312650
%N A211505 Number of solid standard Young tableaux of shape [[(3)^n],[3]].
%C A211505 a(n) is odd if and only if n = 2^k-1, k in {1, 2, 3, ... }.
%H A211505 Alois P. Heinz, <a href="/A211505/b211505.txt">Table of n, a(n) for n = 1..700</a>
%H A211505 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 A211505 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A211505 a(n) = (600 + 2874*n + 4709*n^2 + 3246*n^3 + 1019*n^4 + 144*n^5 + 8*n^6)*(2+3*n)! / (2*(3+2*n)*(5+2*n)*(n-1)!*(2+n)!*(5+n)!). - _Vaclav Kotesovec_, Jul 16 2014
%p A211505 a:=proc(n) option remember; `if`(n<3, [5, 192][n],
%p A211505    ((-300307980720421134*n^6 -450257143569814251*n^5 +520721206232593545*n^4
%p A211505     +237675576478617990*n^3 -244917832991741721*n^2 +20947752092648421*n
%p A211505     +7263907687560150)*a(n-2) +(20284627624231332*n^6 +74969736339564876*n^5
%p A211505     -90577816139486502*n^4 -578021108537112633*n^3 -713543105276625459*n^2
%p A211505     -309855589348004634*n -29055630750240600)*a(n-1)) / (339337400732270*n^6
%p A211505     +2086412513047793*n^5 -1761594949059583*n^4 -24340927184757907*n^3
%p A211505     -25005499944921313*n^2 +25705682578023740*n +29939073413286900))
%p A211505    end:
%p A211505 seq(a(n), n=1..20);
%t A211505 Table[(600 + 2874*n + 4709*n^2 + 3246*n^3 + 1019*n^4 + 144*n^5 + 8*n^6)*(2+3*n)! / (2*(3+2*n)*(5+2*n)*(n-1)!*(2+n)!*(5+n)!), {n, 1, 20}] (* _Vaclav Kotesovec_, Jul 16 2014 *)
%Y A211505 Row n=3 of A214722.
%Y A211505 Cf. A000225.
%K A211505 nonn
%O A211505 1,1
%A A211505 _Alois P. Heinz_, Aug 06 2012