A090588 Number of labeled idempotent groupoids.

1, 1, 4, 729, 16777216, 95367431640625, 221073919720733357899776, 311973482284542371301330321821976049, 374144419156711147060143317175368453031918731001856, 507528786056415600719754159741696356908742250191663887263627442114881

Offset: 0

Author

Christian G. Bower, Dec 03 2003

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..26
• Index entries for sequences related to groupoids

Crossrefs

Cf. A002489, A030247, A076113.

Programs

Magma

[n^(n^2 - n): n in [0..10]]; // Vincenzo Librandi, Aug 08 2015

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 *)

PARI

a(n) = n^(n^2-n); \\ Joerg Arndt, Nov 04 2013

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

Formula

a(n) = n^(n^2 - n).

Extensions

One additional term from Harvey P. Dale, Sep 16 2013