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%I #7 Oct 02 2017 08:25:54
%S 1,4,2,8,16,64,32,64,128,512,256,2048,8192,16384,4096,65536,32768,
%T 131072,65536,262144,524288,2097152,1048576,2097152,4194304,16777216,
%U 8388608,134217728,134217728,1073741824,134217728,536870912,2147483648
%N Largest 2^x dividing A001623(n), the number of reduced three-line Latin rectangles.
%H John Riordan, <a href="http://www.jstor.org/stable/2308187">A recurrence relation for three-line Latin rectangles</a>, Amer. Math. Monthly, 59 (1952), pp. 159-162.
%H D. S. Stones, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v17i1a1/0">The many formulas for the number of Latin rectangles</a>, Electron. J. Combin 17 (2010), A1.
%H D. S. Stones and I. M. Wanless, <a href="http://dx.doi.org/10.1016/j.jcta.2009.03.019">Divisors of the number of Latin rectangles</a>, J. Combin. Theory Ser. A 117 (2010), 204-215.
%F a(n) = A006519(A001623(n)). - _Michel Marcus_, Oct 02 2017
%o (PARI) a001623(n) = n*(n-3)!*sum(i=0, n, sum(j=0, n-i, (-1)^j*binomial(3*i+j+2, j)<<(n-i-j)/(n-i-j)!)*i!);
%o a(n) = 2^valuation(a001623(n), 2); \\ _Michel Marcus_, Oct 02 2017
%Y Cf. A001623, A006519, A130077, A130079.
%K nonn
%O 3,2
%A Douglas Stones (dssto1(AT)student.monash.edu.au), May 06 2007
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