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A000536
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Number of 3-line Latin rectangles.
(Formerly M5152 N2236)
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0
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24, 240, 2520, 26880, 304080, 3671136, 47391120, 653463360, 9603708840, 150046937040, 2485510331304, 43536519673920, 804343214307360, 15636586027419840, 319143375070100640, 6824486562845878656, 152599994618389811640, 3561710724832153990320, 86627571138529803385080, 2192153071078356814538880, 57633178354598014299807984, 1572073330365520093029415200, 44434609885866805678475703600, 1299879247128621094998213278400, 39312834919322919649653205283400, 1227895179113516869799082638629776, 39569125440836907870479047149487560, 1314368274045259508166257769617810880, 44963797526832537006635800892057862720, 1582832153412276057834241761650127323520
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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4,1
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REFERENCES
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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/
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 210.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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