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A001425
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Number of commutative groupoids with n elements.
(Formerly M3714 N1518)
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14
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1, 1, 4, 129, 43968, 254429900, 30468670170912, 91267244789189735259, 8048575431238519331999571800, 24051927835861852500932966021650993560, 2755731922430783367615449408031031255131879354330
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| Satoh, S.; Yama, K.; and Tokizawa, M., Semigroups of order 8, Semigroup Forum 49 (1994), 7-29. [Background]
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
| Eric Postpischil Posting to sci.math newsgroup, May 21 1990
Index entries for sequences related to groupoids
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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*s2!*...)) where fix A[s_1, s_2, ...] = prod {i>=j>=1} f(i, j, s_i, s_j) where f(i, j, s_i, s_j) = {i=j, odd} (sum {d|i} (d*s_d))^((i*s_i^2+s_i)/2) or {i=j, even} (sum {d|i} (d*s_d))^(i*s_i^2/2) * (sum {d|i/2} (d*s_d))^s_i or {i != j} (sum {d|lcm(i, j)} (d*s_d))^(2*gcd(i, j)*s_i*s_j)
a(n) asymptotic to (n^binomial(n+1, 2))/n! = A023813(n)/A000142(n) ~ e^n*n^binomial(n, 2) / sqrt(2*pi*n).
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CROSSREFS
| a(n)+A079183(n)=A001329(n)
Cf. A001329, A023813, A038016.
Sequence in context: A041495 A188315 A117897 * A050284 A096759 A006103
Adjacent sequences: A001422 A001423 A001424 * A001426 A001427 A001428
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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
| More terms from Christian G. Bower (bowerc(AT)usa.net) Feb 15 1998 and May 15 1998. Formula Dec 03 2003.
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