0,3

The number of isomorphism classes of closed binary operations on a set of order n.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

M. A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc., 17 (1966), 731-737.

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.

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

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)

Cf. A001424, A001425, A002489, A006448, A029850, A030245-A030265, A030271, A038015-A038023.

Sequence in context: A123377 A061543 A133198 this_sequence A007101 A007103 A006903

Adjacent sequences: A001326 A001327 A001328 this_sequence A001330 A001331 A001332

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

Formula and more terms from Christian G. Bower (bowerc(AT)usa.net), May 08 1998, Dec 03 2003.