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A215301 Number of solid standard Young tableaux of shape [[n,n-5],[5]].

%I A215301 #18 Jul 19 2017 20:49:12
%S A215301 42,1452,22689,245962,2149454,16290708,111709178,711996820,4292788212,
%T A215301 24777783256,138077129921,747501664986,3949741123174,20444004524804,
%U A215301 103955714523390,520494659493180,2570907398453580,12546842041060200,60579487688891610,289692893191143876
%N A215301 Number of solid standard Young tableaux of shape [[n,n-5],[5]].
%H A215301 Alois P. Heinz, <a href="/A215301/b215301.txt">Table of n, a(n) for n = 5..500</a>
%H A215301 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 A215301 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F A215301 See Maple program.
%F A215301 For n > 6, a(n) = (2*(n-6))! / (5 * (n-6)! * (n+1)!) * 64 * (-51975 + 217350*n - 873908*n^2 + 1738396*n^3 - 2038350*n^4 + 1500940*n^5 - 724004*n^6 + 231788*n^7 - 48750*n^8 + 6460*n^9 - 488*n^10 + 16*n^11). - _Vaclav Kotesovec_, Sep 02 2014
%p A215301 a:=proc(n) option remember; `if`(n<7, [0$4, 42, 1452, 22689][n],
%p A215301    ((-940984202308081409937789248*n^7+36378423601372783158274124928*n^6
%p A215301     -540987251973268278464961515672*n^5+4140452478540141056223108638628*n^4
%p A215301     -17643038551017281385645661643624*n^3+40489345935054116443261823323140*n^2
%p A215301     -39934974057986427003556989745680*n-247683783218781902433156798480)*a(n-1)
%p A215301     +(5038765510419498883689330496*n^7-154613008671019208064714735488*n^6
%p A215301     +1939670093038831522623368803072*n^5-12888788321486668402366527701360*n^4
%p A215301 +48941495657518683977159471709724*n^3-105016281014420890409086708155812*n^2
%p A215301     +113403222542936117699329884355248*n-47046838608769352958257951122560)
%p A215301     *a(n-2))/(79676793824198327746135844*n^7-1949805875384464242394656236*n^6
%p A215301     +20900166698905174940775960603*n^5-125515785015357799830976856812*n^4
%p A215301     +431332553464051479008795376439*n^3-723271251684163430971195319466*n^2
%p A215301     +59211568171613916060478086240*n+1362260807703300463382362391640))
%p A215301    end:
%p A215301 seq(a(n), n=5..30);
%t A215301 Flatten[{42, 1452, Table[(2*(n-6))! / (5 * (n-6)! * (n+1)!) * 64 * (-51975 + 217350*n - 873908*n^2 + 1738396*n^3 - 2038350*n^4 + 1500940*n^5 - 724004*n^6 + 231788*n^7 - 48750*n^8 + 6460*n^9 - 488*n^10 + 16*n^11), {n, 7, 20}]}]
%Y A215301 Column k=5 of A214775.
%Y A215301 Cf. A215002.
%K A215301 nonn
%O A215301 5,1
%A A215301 _Alois P. Heinz_, Aug 07 2012