Search: id:A002489
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%I A002489 M5030 N2170
%S A002489 1,1,16,19683,4294967296,298023223876953125,
%T A002489 10314424798490535546171949056,256923577521058878088611477224235621321607,
%U A002489 6277101735386680763835789423207666416102355444464034512896,19662705047555291361807590852691211628310345094421\
               4766927315415537966391196809
%N A002489 n^(n^2) (or (n^n)^n).
%C A002489 The number of closed binary operations on a set of order n. Labeled groupoids.
%D A002489 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002489 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002489 J. S. Rose, A Course on Group Theory, Camb. Univ. Press, 1978, see p. 
               6.
%D A002489 P. Rossier, Grands nombres, Elemente der Mathematik, 3 (1948), 20.
%H A002489 Eric Postpischil <a href="http://groups.google.com/groups?&hl=en&lr=&ie=UTF-8&selm=11802%40shlump.nac.dec.com\
               &rnum=2">Posting to sci.math newsgroup, May 21 1990</a>
%H A002489 <a href="Sindx_Gre.html#groupoids">Index entries for sequences related 
               to groupoids</a>
%e A002489 a(3) = 19683 because (3^3)^3 = 3^(3^2) = 19683.
%p A002489 seq(mul(mul(j*n/k,j=1..n), k=1..n), n=0..9); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 02 2007
%p A002489 a:=n->mul(mul(sum(1, j=1..n), k=1..n), m=1..n): seq(a(n), n=0..9);# [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 31 2008]
%Y A002489 a(n)=A079172(n)+A023814(n)=A079176(n)+A079179(n)
%Y A002489 a(n)=A079182(n)+A023813(n)=A079186(n)+A079189(n)
%Y A002489 a(n)=A079192(n)+A079195(n)+A079198(n)+A023185(n)
%Y A002489 Cf. A002488.
%Y A002489 Cf. A001329, A002488, A023813, A076113, A090588
%Y A002489 Sequence in context: A159387 A098175 A089232 this_sequence A060205 A140597 
               A017296
%Y A002489 Adjacent sequences: A002486 A002487 A002488 this_sequence A002490 A002491 
               A002492
%K A002489 nonn,easy,nice
%O A002489 0,3
%A A002489 N. J. A. Sloane (njas(AT)research.att.com).

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