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Search: id:A113547
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| A113547 |
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Triangle read by rows: number of labeled partitions of n with maximin m. |
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1
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| 1, 1, 1, 1, 2, 2, 1, 4, 5, 5, 1, 8, 13, 15, 15, 1, 16, 35, 47, 52, 52, 1, 32, 97, 153, 188, 203, 203, 1, 64, 275, 515, 706, 825, 877, 877, 1, 128, 793, 1785, 2744, 3479, 3937, 4140, 4140, 1, 256, 2315, 6347, 11002, 15177, 18313, 20270, 21147, 21147, 1, 512, 6817
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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The maximin of a partition is the maximum over all parts of the minimum label in each part. If the rows are reversed, the result is the number of partitions of n with minimax m.
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FORMULA
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T(n, m)=Sum_{k=1}^m S2(m, k-1)*k^(n-m), where S2 is the Stirling numbers of the second kind (A08277). T(n, n)=T(n, n-1)=B(n-1), where B is the Bell numbers (A000110). T(n, n-2)=B(n-1)-B(n-3).
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EXAMPLE
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Maximin [123]=max(1)=1, maximin [12|3]=max(1,3)=3, maximin [13|2]=max(1,2)=2, maximin [1|23]=max(1,2)=2, and maximin [1|2|3]=max(1,2,3)=3, so for n=3 the multiset of maximins is {1,2,2,3,3}, making the 3rd line 1,2,2.
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CROSSREFS
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Cf. A008277, A000110.
Sequence in context: A064189 A063415 A098977 this_sequence A115313 A048942 A121484
Adjacent sequences: A113544 A113545 A113546 this_sequence A113548 A113549 A113550
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KEYWORD
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nonn,tabl
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 2006
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