Search: id:A001329
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%I A001329 M4760 N2035
%S A001329 1,1,10,3330,178981952,2483527537094825,14325590003318891522275680,
%T A001329 50976900301814584087291487087214170039,
%U A001329 155682086691137947272042502251643461917498835481022016
%N A001329 Number of nonisomorphic groupoids with n elements.
%C A001329 The number of isomorphism classes of closed binary operations on a set 
               of order n.
%D A001329 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001329 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001329 M. A. Harrison, The number of isomorphism types of finite algebras, Proc. 
               Amer. Math. Soc., 17 (1966), 731-737.
%D A001329 T. Tamura, Some contributions of computation to semigroups and groupoids, 
               pp. 229-261 of J. Leech, editor, Computational Problems in Abstract 
               Algebra. Pergamon, Oxford, 1970.
%H A001329 Eric Postpischil, <a href="http://groups.google.com/groups?&hl=en&lr=&ie=UTF-8&selm=11802%40shlump.nac.dec.co\
               m&rnum=2">Posting to sci.math newsgroup, May 21 1990</a>
%H A001329 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Groupoid.html">Link to a section of The World of Mathematics.</a>
%H A001329 <a href="Sindx_Gre.html#groupoids">Index entries for sequences related 
               to groupoids</a>
%F A001329 a[ n ]=prod{i, j >= 1}(sum{d|[ i, j ]}(d*n(d))^((i, j)*n(i)*n(j)))
%F A001329 a(n) = sum {1*s_1+2*s_2+...=n} (fix A[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s2!*...)) 
               where fix A[s_1, s_2, ...] = prod {i, j>=1} ( (sum {d|lcm(i, j)} 
               (d*s_d))^(gcd(i, j)*s_i*s_j))
%F A001329 a(n) asymptotic to n^(n^2)/n! = A002489(n)/A000142(n) ~ (e*n^(n-1))^n 
               / sqrt(2*pi*n).
%Y A001329 a(n)=A079173(n)+A027851(n)=A079177(n)+A079180(n)
%Y A001329 a(n)=A079183(n)+A001425(n)=A079187(n)+A079190(n)
%Y A001329 a(n)=A079193(n)+A079196(n)+A079199(n)+A001426(n)
%Y A001329 Cf. A001424, A001425, A002489, A006448, A029850, A030245-A030265, A030271, 
               A038015-A038023.
%Y A001329 Sequence in context: A123377 A061543 A133198 this_sequence A007101 A007103 
               A006903
%Y A001329 Adjacent sequences: A001326 A001327 A001328 this_sequence A001330 A001331 
               A001332
%K A001329 nonn,nice
%O A001329 0,3
%A A001329 N. J. A. Sloane (njas(AT)research.att.com).
%E A001329 Formula and more terms from Christian G. Bower (bowerc(AT)usa.net), May 
               08 1998, Dec 03 2003.

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