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A260331
Labelings of n diamond-shaped posets with 4 vertices per diamond where the labels follow the poset relations.
4
1, 2, 280, 277200, 1009008000, 9777287520000, 207786914375040000, 8508874143657888000000, 611958228411875304960000000, 72094798889203029677337600000000, 13177487340968529764423766528000000000, 3577714168047637768100581459885056000000000, 1392303245637418713834022280928868392960000000000
OFFSET
0,2
COMMENTS
By diamond-shaped poset with 4 vertices, we mean a poset on four elements with e_1 < e_2, e_1 < e_3, e_2 < e_4, e_3 < e_4, and no order relations between e_2 and e_3. In the Hasse diagram for such a poset, we have a least element, two elements in the level above, and one element in the top level, so the diagram resembles a diamond.
FORMULA
a(n) = (4n)!/12^n.
EXAMPLE
For a single diamond (n=1) poset with 4 vertices, we must label the least element 1 and the greatest element 4, and the two central elements can be labeled either 2, 3 or 3, 2 respectively. Thus the associated permutations are 1234 and 1324.
MATHEMATICA
Table[(4 n)!/12^n, {n, 0, 12}] (* Michael De Vlieger, Apr 06 2016 *)
CROSSREFS
Sequence in context: A172374 A231041 A080296 * A307470 A182519 A279450
KEYWORD
nonn
AUTHOR
Manda Riehl, Jul 29 2015
EXTENSIONS
More terms from Michael De Vlieger, Apr 06 2016
a(4) corrected by Georg Fischer, May 08 2021
STATUS
approved