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Search: id:A101880
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| A101880 |
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Number of arrangments of the partitions of n (e.g. 111 counts for 6). |
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+0
1
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| 1, 3, 9, 35, 161, 913, 6103, 47319, 416235, 4092155, 44424095, 527511445, 6798907249, 94504286703, 1408973416617, 22426222745159, 379522092608177, 6804315177704869, 128828842646944135, 2568533750228603835
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Jon Perry, Partition Tables
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FORMULA
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a(n) = sum(i=1, n, P(n, i)*i!), where P(n, i) is the number of partitions of n into i parts.
G.f.: Sum(n!*x^n/Product(1-x^k, k=1..n), n=1..infinity). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 29 2005
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EXAMPLE
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a(3)=9 as we have 3, 12 (2) and 111 (6).
a(4)=35 as 4, 31 (2), 22 (2), 211 (6) and 1111 (24)
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MATHEMATICA
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Rest[ CoefficientList[ Series[ Sum[ n!x^n / Product[1 - x^k, {k, n}], {n, 20}], {x, 0, 20}], x]] (from Robert G. Wilson v Feb 10 2005)
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CROSSREFS
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Sequence in context: A030268 A097277 A034428 this_sequence A107894 A000834 A005346
Adjacent sequences: A101877 A101878 A101879 this_sequence A101881 A101882 A101883
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KEYWORD
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nonn,nice
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Jan 28 2005
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 29 2005
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