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A023813 a(n) = n^(n*(n+1)/2).

%I A023813 #43 Aug 06 2018 08:52:28
%S A023813 1,1,8,729,1048576,30517578125,21936950640377856,
%T A023813 459986536544739960976801,324518553658426726783156020576256,
%U A023813 8727963568087712425891397479476727340041449,10000000000000000000000000000000000000000000000000000000
%N A023813 a(n) = n^(n*(n+1)/2).
%C A023813 Determinant of n X n matrix M_(i,j) = binomial(n*i,j). - _Benoit Cloitre_, Sep 13 2003
%C A023813 Number of commutative binary operations on an n-set. Labeled commutative groupoids.
%H A023813 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 A023813 <a href="/index/Gre#groupoids">Index entries for sequences related to groupoids</a>
%F A023813 a(n) = Product_{k=1..n} n^k. - _José de Jesús Camacho Medina_, Jul 12 2016
%F A023813 a(n) = n^A000217(n). - _Alois P. Heinz_, Aug 06 2018
%p A023813 seq(mul(n^k, k=1..n), n=0..10); # _Zerinvary Lajos_, Jun 03 2007
%t A023813 Table[n^((n^2 + n)/2), {n, 1, 10}]  (* _Geoffrey Critzer_, Jan 27 2013 *)
%Y A023813 a(n) + A079182(n) = A002489(n).
%Y A023813 Cf. A000217, A001425, A002489, A023814, A023815.
%K A023813 easy,nonn
%O A023813 0,3
%A A023813 Lyle Ramshaw (ramshaw(AT)pa.dec.com)
%E A023813 Better description from _Amarnath Murthy_, Dec 29 2001