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Search: id:A114868
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| 1, 0, 0, 1, 1, 1, 1, 2, 3, 2, 3, 4, 7, 6, 7, 10, 17, 14, 18, 26, 41, 36, 44, 64, 104, 91, 112, 163
(list; graph; listen)
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OFFSET
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1,8
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COMMENT
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This sequence is an approximation of a quadruple factorial analogue to Stirling's approximation to factorial. Note that a(n) is exact for n = 1, 4, 8.
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FORMULA
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a(n) = Floor[n^(n/4)/n!!! ]. a(n) = Floor[4thRoot(A000312(n))/A007662(n)].
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EXAMPLE
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a(8) = Floor[(8^2)/8!!!! ] = Floor[(8^2)/32] = Floor[2] = 2.
a(9) = Floor[(9^2.25)/9!!!! ] = Floor[(9^2.25)/45] = Floor[3.11769145] = 3.
a(16) = Floor[(16^4)/16!!!! ] = Floor[(16^4)/6144] = Floor[10.6666667] = 10.
a(20) = Floor[(20^5)/20!!!! ] = Floor[(20^5)/122880] = Floor[26.0416667] = 26.
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CROSSREFS
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Cf. A000312, A006882, A055775, A007662.
Sequence in context: A026342 A078198 A098235 this_sequence A138239 A112484 A080092
Adjacent sequences: A114865 A114866 A114867 this_sequence A114869 A114870 A114871
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 20 2006
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