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Search: id:A048775
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| A048775 |
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Number of (partially defined) monotone maps from intervals of 1..n to 1..n. |
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+0
3
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| 1, 7, 31, 121, 456, 1709, 6427, 24301, 92368, 352705, 1352066, 5200287, 20058286, 77558745, 300540179, 1166803093, 4537567632, 17672631881, 68923264390, 269128937199, 1052049481838, 4116715363777
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Arises in the classification of endomorphisms of certain finite-dimensional operator algebras.
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FORMULA
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Binomial(2*r+1, r+1)-(r+1)
a(n) = Sum[Sum[(i+j)!/i!/j!,{i,1,n}],{j,1,n}]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006
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EXAMPLE
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a(2) = 7 because there are two maps with domain {1}, two with domain {2} and three maps with domain {1,2}.
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MATHEMATICA
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Table[Sum[Sum[(i+j)!/i!/j!, {i, 1, n}], {j, 1, n}], {n, 1, 20}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006
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CROSSREFS
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Cf. A001700.
Sequence in context: A032197 A114289 A147597 this_sequence A125193 A002184 A002588
Adjacent sequences: A048772 A048773 A048774 this_sequence A048776 A048777 A048778
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Stephen C. Power (s.power(AT)lancaster.ac.uk)
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