A130077 - OEIS

%I #7 Oct 02 2017 08:25:48

%S 0,2,1,3,4,6,5,6,7,9,8,11,13,14,12,16,15,17,16,18,19,21,20,21,22,24,

%T 23,27,27,30,27,29,31,33,32,34,35,37,36,37,38,40,39,42,44,45,43,50,46,

%U 48,47,49,50,52,51,52,53,55,54,59,58,62,58,60,63,65,64,66,67,69,68,69,70

%N Largest x such that 2^x divides 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) = A007814(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) = valuation(a001623(n), 2); \\ _Michel Marcus_, Oct 02 2017

%Y Cf. A001623, A007814, A130078, A130079.

%K nonn

%O 3,2

%A Douglas Stones (dssto1(AT)student.monash.edu.au), May 06 2007