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A090602 Number of n-element labeled groupoids with an identity.

%I A090602 #16 Feb 16 2025 08:32:52
%S A090602 0,1,4,243,1048576,762939453125,170581728179578208256,
%T A090602 18562115921017574302453163671207,
%U A090602 1427247692705959881058285969449495136382746624,106111661199647248543687855752712667991103904330482569981872649
%N A090602 Number of n-element labeled groupoids with an identity.
%C A090602 Also labeled groupoids with an absorbant (zero) element.
%H A090602 Andrew Howroyd, <a href="/A090602/b090602.txt">Table of n, a(n) for n = 0..20</a>
%H A090602 Eric Postpischil <a href="http://groups.google.com/groups?&amp;hl=en&amp;lr=&amp;ie=UTF-8&amp;selm=11802%40shlump.nac.dec.com&amp;rnum=2">Posting to sci.math newsgroup, May 21 1990</a>
%H A090602 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Groupoid.html">Groupoid</a>
%H A090602 Wikipedia, <a href="https://en.wikipedia.org/wiki/Magma_(algebra)">Magma (algebra)</a>
%H A090602 <a href="/index/Gre#groupoids">Index entries for sequences related to groupoids</a>
%F A090602 a(n) = n^((n-1)^2+1).
%F A090602 a(n) = A090603(n)*n.
%o A090602 (PARI) a(n) = n^((n-1)^2+1) \\ _Andrew Howroyd_, Jan 23 2022
%Y A090602 Cf. A090601 (isomorphism classes), A090603.
%K A090602 nonn
%O A090602 0,3
%A A090602 _Christian G. Bower_, Dec 05 2003
%E A090602 a(0)=0 prepended and a(9) added by _Andrew Howroyd_, Jan 23 2022