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Search: id:A006448
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| A006448 |
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Number of n-element algebras with 1 binary operator and 1 constant (pointed groupoids).
(Formerly M5029)
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+0
3
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| 1, 16, 9882, 715860992, 12417636281312500, 85953540009068492207916672, 356838302112667713247240882121025536249, 1245456693529103515171728481423145699858332531028201472
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc., 17 (1966), 731-737.
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LINKS
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Index entries for sequences related to groupoids
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FORMULA
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F[ n ]=n(1)*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, ...] = s_1 * 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+1)/n!
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CROSSREFS
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Cf. A001329.
Sequence in context: A079920 A069986 A151641 this_sequence A017092 A167062 A017188
Adjacent sequences: A006445 A006446 A006447 this_sequence A006449 A006450 A006451
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Formula and more terms from Christian G. Bower (bowerc(AT)usa.net), May 08 1998, Dec 03 2003.
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