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Search: id:A090601
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| A090601 |
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Number of n-element groupoids with an identity. |
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+0
3
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| 1, 2, 45, 43968, 6358196250, 236919104155855296, 3682959509036574988532481464, 35398008251644050232134479709365068115968, 292415292106611727928759157427747328169866020125762652311
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also partial groupoids with n-1 elements or groupoids with an absorbant (zero) element with n elements.
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LINKS
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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
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FORMULA
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a(n+1) = 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} ( (1 + sum {d|lcm(i, j)} (d*s_d))^(gcd(i, j)*s_i*s_j))
a(n) asymptotic to n^((n-1)^2+1)/n! = A090602(n)/A000142(n) = A090603(n)/A000142(n-1)
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CROSSREFS
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Adjacent sequences: A090598 A090599 A090600 this_sequence A090602 A090603 A090604
Sequence in context: A019579 A092654 A100101 this_sequence A071777 A066555 A012001
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KEYWORD
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nonn
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Dec 05 2003
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