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A090588
Number of labeled idempotent groupoids.
6
1, 1, 4, 729, 16777216, 95367431640625, 221073919720733357899776, 311973482284542371301330321821976049, 374144419156711147060143317175368453031918731001856, 507528786056415600719754159741696356908742250191663887263627442114881
OFFSET
0,3
FORMULA
a(n) = n^(n^2 - n).
MAPLE
a:=n->mul(mul(sum(1, j=1..n), k=1..n), m=1..n-1): seq(a(n), n=0..8); # Zerinvary Lajos, Dec 31 2008
MATHEMATICA
Join[{1}, Table[n^(n^2-n), {n, 10}]] (* Harvey P. Dale, Sep 16 2013 *)
PROG
(Ruby)
def a(n)
ids =* (0..n-1)
return (ids.product(ids)).reduce(1){ |accum, x| (x[0] == x[1]) ? accum : accum*ids.length}
end
# Chad Brewbaker, Nov 03 2013
(PARI) a(n) = n^(n^2-n); \\ Joerg Arndt, Nov 04 2013
(Magma) [n^(n^2 - n): n in [0..10]]; // Vincenzo Librandi, Aug 08 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Dec 03 2003
EXTENSIONS
One additional term from Harvey P. Dale, Sep 16 2013
STATUS
approved