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%I M5152 N2236 #26 Feb 09 2016 08:36:44
%S 24,240,2520,26880,304080,3671136,47391120,653463360,9603708840,
%T 150046937040,2485510331304,43536519673920,804343214307360,
%U 15636586027419840,319143375070100640,6824486562845878656,152599994618389811640,3561710724832153990320,86627571138529803385080,2192153071078356814538880,57633178354598014299807984,1572073330365520093029415200,44434609885866805678475703600,1299879247128621094998213278400,39312834919322919649653205283400,1227895179113516869799082638629776,39569125440836907870479047149487560,1314368274045259508166257769617810880,44963797526832537006635800892057862720,1582832153412276057834241761650127323520
%N Number of 3-line Latin rectangles.
%D Eggleton, Roger B. "Maximal Midpoint-Free Subsets of Integers." International Journal of Combinatorics Volume 2015, Article ID 216475, 14 pages; http://dx.doi.org/10.1155/2015/216475; http://www.hindawi.com/journals/ijcom/2015/216475/abs/
%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 210.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>
%F Let K(0,0)=1; K(n,0)=n*K(n-1,0)+(-1)^n, n>0; and j*K(n,j)=n*(n+1-2*j)*K(n-1,j-1)+n*(n-1)*K(n-2,j-1), j>0. Sequence is a(n)=K(n,2). - _Sean A. Irvine_, Nov 15 2010
%t K[0, 0] = 1; K[n_, 0] := K[n, 0] = n*K[n-1, 0] + (-1)^n; K[n_, j_] := K[n, j] = (1/j)(n*(n+1-2*j)*K[n-1, j-1] + n*(n-1)*K[n-2, j-1]); a[n_] := K[n, 2]; Table[a[n], {n, 4, 33}] (* _Jean-François Alcover_, Feb 09 2016, after _Sean A. Irvine_ *)
%K nonn
%O 4,1
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Nov 15 2010
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