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A140188
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Table read by rows: T(n,k) is the number of groupoids (categories all of whose morphisms are invertible) with n morphisms and k objects.
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5
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1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 3, 3, 1, 1, 2, 4, 5, 3, 1, 1, 1, 5, 6, 5, 3, 1, 1, 5, 8, 10, 9, 5, 3, 1, 1, 2, 10, 14, 12, 9, 5, 3, 1, 1, 2, 13, 21, 20, 15, 9, 5, 3, 1, 1, 1, 13, 24, 29, 23, 15, 9, 5, 3, 1, 1, 5, 20, 39, 42, 37, 27, 15, 9, 5, 3, 1, 1, 1, 19, 43, 58, 53, 40, 27, 15, 9, 5, 3, 1, 1, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| The first column is T(n,1) = A00001(n) (number of groups of order n).
T(n,k) >= A136406(n,k).
The sum of the n^th row is A140189(n).
For 2k<=n, T(n,n-k) = A140190(k) does not depend on n.
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LINKS
| B. Jubin, Sequences contributed to the OEIS.
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FORMULA
| T(n,k) is the sum over the quadratic bi-partitions (n_i,k_i) of (n,k) (see A136406) of the "product" of the A000001(n_i), where the "product" is the usual product except when (n_i1,k_i1)=...=(n_ip,k_ip), in which case a^p is replaced by binom(a+p-1,p).
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CROSSREFS
| Cf. A140185.
Sequence in context: A100619 A094006 A179617 * A180050 A202603 A140737
Adjacent sequences: A140185 A140186 A140187 * A140189 A140190 A140191
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KEYWORD
| nonn,tabl
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AUTHOR
| Benoit Jubin (benoit_jubin(AT)yahoo.fr), May 12 2008
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