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%I M5281 #40 Feb 27 2018 13:23:57
%S 1,1,42,6006,1662804,701149020,396499770810,278607172289160,
%T 231471904322784840,219738059326729823880,232553551737813227594400,
%U 269396678720275351794712800,336839101096824285057473785200,449620757769949216266129125515200
%N 5-dimensional Catalan numbers.
%C Number of standard tableaux of shape (n,n,n,n,n). - _Emeric Deutsch_, May 13 2004
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D Snover, Stephen L.; Troyer, Stephanie F.; A four-dimensional Catalan formula. Proceedings of the Nineteenth Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, MB, 1989). Congr. Numer. 75 (1990), 123-126.
%H Alois P. Heinz, <a href="/A005791/b005791.txt">Table of n, a(n) for n = 0..294</a>
%H Shalosh B. Ekhad and Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/ssyt.html">Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux</a>. Also arXiv preprint arXiv:1202.6229, 2012. - _N. J. A. Sloane_, Jul 07 2012
%H K. Gorska and K. A. Penson, <a href="http://arxiv.org/abs/1304.6008">Multidimensional Catalan and related numbers as Hausdorff moments</a>, arXiv preprint arXiv:1304.6008 [math.CO], 2013, and Prob. Math. Stat. 33 (2) (2013) 265-274.
%H S. Snover, <a href="/A005789/a005789.pdf">Letter to N. J. A. Sloane, May 1991</a>
%H S. F. Troyer & S. L. Snover, <a href="/A005789/a005789_1.pdf">m-Dimensional Catalan numbers</a>, Preprint, 1989. (Annotated scanned copy)
%F a(n) = 0!*1!*..*(k-1)! *(k*n)! / ( n!*(n+1)!*..*(n+k-1)! ) for k=5.
%F (n+4)*(n+3)*(n+2)*(n+1)*a(n) -5*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1)=0. - _R. J. Mathar_, Aug 10 2015
%F G.f.: x*5F4(1,6/5,7/5,8/5,9/5;3,4,5,6;3125*x). - _R. J. Mathar_, Aug 10 2015
%F a(n) ~ 72*5^(5*n+1/2)/(Pi^2*n^12). - _Vaclav Kotesovec_, Nov 18 2016
%F E.g.f.: 4F4(1/5,2/5,3/5,4/5; 2,3,4,5; 3125*x). - _Ilya Gutkovskiy_, Oct 13 2017
%p a:= n-> (5*n)! * mul(i!/(n+i)!, i=0..4):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Jul 23 2017
%t Table[288*(5*n)!/(n!*(n+1)!*(n+2)!*(n+3)!*(n+4)!), {n, 1, 20}] (* _Vaclav Kotesovec_, Nov 18 2016 *)
%Y A row of A060854.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_.
%E a(0)=1 prepended by _Alois P. Heinz_, Jul 23 2017
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