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A001330
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Number of n-element algebras with 2 binary operations.
(Formerly M5398 N2346)
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0
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1, 1, 136, 64573605, 768614338015543296, 740148683083442627372862307855625, 147760220727384062234340471228346859265417269763446784, 13097167596472133103922286145973062271265962292695709182416029922453889335720758
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Isomorphisms classes of a set A with two functions f1,f2: A X A -> A.
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REFERENCES
| M. A. Harrison, The number of isomorphism types of finite algebras, Proc. Amer. Math. Soc., 17 (1966), 731-737.
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).
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FORMULA
| a(n) = sum {1*s_1+2*s_2+...=n} (fix A[s_1, s_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...)) where fix A[s_1, s_2, ...] = Product_{i, j>=1} ( (sum {d|lcm(i, j)} (d*s_d))^(gcd(i, j)*s_i*s_j*2)).
a(n) is asymptotic to n^(2*n^2)/n! = A008972(n)/A000142(n).
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CROSSREFS
| Cf. A001329, A001331.
Sequence in context: A194014 A035819 A157880 * A091510 A134885 A082726
Adjacent sequences: A001327 A001328 A001329 * A001331 A001332 A001333
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited and extended with formula by Christian G. Bower (bowerc(AT)usa.net), Jan 06 2004
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