login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A000536
Number of 3-line Latin rectangles.
(Formerly M5152 N2236)
0
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
OFFSET
4,1
REFERENCES
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).
FORMULA
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
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A052520 A052724 A357242 * A151720 A052652 A052732
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Nov 15 2010
STATUS
approved