cp's OEIS Frontend

A090588 Number of labeled idempotent groupoids.

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