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A001329
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Number of nonisomorphic groupoids with n elements.
(Formerly M4760 N2035)
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42
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1, 1, 10, 3330, 178981952, 2483527537094825, 14325590003318891522275680, 50976900301814584087291487087214170039, 155682086691137947272042502251643461917498835481022016
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The number of isomorphism classes of closed binary operations on a set of order n.
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REFERENCES
| N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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LINKS
| J. Berman and S. Burris, A computer study of 3-element groupoids Lect. Notes Pure Appl. Math. 180 (1994) 379-429 MR1404949
M. A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc., 17 (1966), 731-737.
Eric Postpischil, Posting to sci.math newsgroup, May 21 1990
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to groupoids
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FORMULA
| a[ n ]=prod{i, j >= 1}(sum{d|[ i, j ]}(d*n(d))^((i, j)*n(i)*n(j))).
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)).
a(n) asymptotic to n^(n^2)/n! = A002489(n)/A000142(n) ~ (e*n^(n-1))^n / sqrt(2*pi*n).
a(n)=A079173(n)+A027851(n)=A079177(n)+A079180(n).
a(n)=A079183(n)+A001425(n)=A079187(n)+A079190(n).
a(n)=A079193(n)+A079196(n)+A079199(n)+A001426(n).
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CROSSREFS
| Cf. A001424, A001425, A002489, A006448, A029850, A030245-A030265, A030271, A038015-A038023.
Sequence in context: A123377 A061543 A133198 * A007101 A007103 A006903
Adjacent sequences: A001326 A001327 A001328 * A001330 A001331 A001332
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Formula and more terms from Christian G. Bower (bowerc(AT)usa.net), May 08 1998, Dec 03 2003.
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