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Search: id:A097303
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| A097303 |
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Denominators in Stirling's asymptotic series. |
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+0
2
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| 1, 12, 144, 8640, 103680, 1741824, 104509440, 179159040, 2149908480, 1418939596800, 23838185226240, 338068808663040, 20284128519782400, 18723810941337600, 32097961613721600, 229179445921972224000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Numerators coincide with the numbers depicted in A001163 but differ for the first time at entry nr. 33. See the W. Lang link.
Stirling's formula for GAMMA(z) (|arg(z)|<Pi) uses the asymptotic series sum((N(k)/a(k))*((1/z)^k)/k!,k=0..infinity). For N(k) see the W. Lang link.
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LINKS
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W. Lang, More terms and comments.
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FORMULA
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a(n) = denominator(s(n)), where the signed rationals s(n) are the coefficients of ((1/z)^k)/k! in the asymptotic series appearing in Stirling's formula for GAMMA(z).
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CROSSREFS
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Cf. A001163, A001164 (Stirling formula with further links and references.).
Sequence in context: A143248 A138444 A137886 this_sequence A067219 A075619 A055332
Adjacent sequences: A097300 A097301 A097302 this_sequence A097304 A097305 A097306
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 13 2004
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