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%I #35 Sep 08 2022 08:45:12
%S 1,1,4,729,16777216,95367431640625,221073919720733357899776,
%T 311973482284542371301330321821976049,
%U 374144419156711147060143317175368453031918731001856,507528786056415600719754159741696356908742250191663887263627442114881
%N Number of labeled idempotent groupoids.
%H Alois P. Heinz, <a href="/A090588/b090588.txt">Table of n, a(n) for n = 0..26</a>
%H <a href="/index/Gre#groupoids">Index entries for sequences related to groupoids</a>
%F a(n) = n^(n^2 - n).
%p 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
%t Join[{1},Table[n^(n^2-n),{n,10}]] (* _Harvey P. Dale_, Sep 16 2013 *)
%o (Ruby)
%o def a(n)
%o ids =* (0..n-1)
%o return (ids.product(ids)).reduce(1){ |accum,x| (x[0] == x[1]) ? accum : accum*ids.length}
%o end
%o # _Chad Brewbaker_, Nov 03 2013
%o (PARI) a(n) = n^(n^2-n); \\ _Joerg Arndt_, Nov 04 2013
%o (Magma) [n^(n^2 - n): n in [0..10]]; // _Vincenzo Librandi_, Aug 08 2015
%Y Cf. A002489, A030247, A076113.
%K nonn
%O 0,3
%A _Christian G. Bower_, Dec 03 2003
%E One additional term from _Harvey P. Dale_, Sep 16 2013
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