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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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2
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1, 16, 9882, 715860992, 12417636281312500, 85953540009068492207916672, 356838302112667713247240882121025536249, 1245456693529103515171728481423145699858332531028201472
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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).
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LINKS
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Table of n, a(n) for n=1..8.
M. A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc., 17 (1966), 731-737.
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: A151641 A265240 A221137 * A017092 A265634 A191945
Adjacent sequences: A006445 A006446 A006447 * 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.
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EXTENSIONS
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Formula and more terms from Christian G. Bower, May 08 1998, Dec 03 2003
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STATUS
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approved
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