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a(n) = n^(n*(n+1)/2).
13

%I #43 Aug 06 2018 08:52:28

%S 1,1,8,729,1048576,30517578125,21936950640377856,

%T 459986536544739960976801,324518553658426726783156020576256,

%U 8727963568087712425891397479476727340041449,10000000000000000000000000000000000000000000000000000000

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

%C Determinant of n X n matrix M_(i,j) = binomial(n*i,j). - _Benoit Cloitre_, Sep 13 2003

%C Number of commutative binary operations on an n-set. Labeled commutative groupoids.

%H 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 <a href="/index/Gre#groupoids">Index entries for sequences related to groupoids</a>

%F a(n) = Product_{k=1..n} n^k. - _José de Jesús Camacho Medina_, Jul 12 2016

%F a(n) = n^A000217(n). - _Alois P. Heinz_, Aug 06 2018

%p seq(mul(n^k, k=1..n), n=0..10); # _Zerinvary Lajos_, Jun 03 2007

%t Table[n^((n^2 + n)/2), {n, 1, 10}] (* _Geoffrey Critzer_, Jan 27 2013 *)

%Y a(n) + A079182(n) = A002489(n).

%Y Cf. A000217, A001425, A002489, A023814, A023815.

%K easy,nonn

%O 0,3

%A Lyle Ramshaw (ramshaw(AT)pa.dec.com)

%E Better description from _Amarnath Murthy_, Dec 29 2001