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A122253 Denominator of the n-th series entry for the convergent form of Stirling's Approximation for the gamma function. log gamma z = (z - 1/2) log z - z + log(2*Pi)/2 + sum(c(n)/(z+1)^(n), {n, 1, infinity}], where z^(n) is the rising factorial. 1
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; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..34.

Raphael Schumacher, Rapidly Convergent Summation Formulas involving Stirling Series, arXiv preprint arXiv:1602.00336, 2016

Wikipedia, Stirling's Approximation

FORMULA

c(n) = integral(x^(n)*(x - 1/2), {x, 0, 1}) / n.

EXAMPLE

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.

MATHEMATICA

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;

CROSSREFS

Cf. A001163, A001164, A122252.

Sequence in context: A038338 A221796 A222298 * A156456 A077180 A105745

Adjacent sequences:  A122250 A122251 A122252 * A122254 A122255 A122256

KEYWORD

easy,frac,nonn

AUTHOR

Paul Drees (zemyla(AT)gmail.com), Aug 27 2006

STATUS

approved

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Last modified July 17 02:56 EDT 2019. Contains 325092 sequences. (Running on oeis4.)