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Search: id:A122253
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| A122253 |
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Denominator of the n-th series entry for the convergent form of Stirling's Approximation for the gamma function. ln gamma z = (z - 1/2) ln z - z + ln(2pi)/2 + sum(c(n)/(z+1)^(n), {n, 1, infinity}], where z^(n) is the rising factorial. |
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+0
2
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| 12, 12, 360, 60, 280, 168, 5040, 180, 11880, 264, 240240, 10920, 13104, 720, 367200, 3060, 813960, 15960, 1053360, 27720, 3825360, 16560, 5023200, 163800, 982800, 3024, 2630880, 6960, 33227040, 229152, 116867520, 235620, 282744, 2520
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Wikipedia, Stirling's Approximation
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FORMULA
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c(n) = integral(x^(n)*(x - 1/2), {x, 0, 1}) / n
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EXAMPLE
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c(1) = integral(x*(x - 1/2), {x, 0, 1}) / 1 = integral(x^2 - x/2, {x, 0, 1}) = x^3/3 - x^2/4|{x, 0, 1} = 1/12
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MATHEMATICA
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Rising[z_, n_Integer/; n>0] := z Rising[z + 1, n - 1]; Rising[z_, 0] := 1; c[n_Integer/; n>0] := Integrate[Rising[x, n] (x - 1/2), {x, 0, 1}] / n;
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CROSSREFS
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Cf. A001163, A001164, A122252.
Sequence in context: A067123 A165833 A038338 this_sequence A156456 A077180 A105745
Adjacent sequences: A122250 A122251 A122252 this_sequence A122254 A122255 A122256
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Paul Drees (zemyla(AT)gmail.com), Aug 27 2006
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