login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A182913 Denominators of an asymptotic series for the Gamma function (G. Nemes) 3
1, 1, 144, 12960, 207360, 2612736, 9405849600, 18811699200, 1083553873920, 4022693756928000, 300361133850624000, 210853515963138048000, 151814531493459394560000, 151814531493459394560000, 21861292535058152816640000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

G_n = A182912(n)/A182913(n). These rational numbers provide the coefficients for an asymptotic expansion of the Gamma function.

REFERENCES

G. Nemes, More Accurate Approximations for the Gamma Function,

Thai Journal of Mathematics Volume 9(1) (2011), 21-28.

LINKS

Table of n, a(n) for n=0..14.

Peter Luschny, Approximation Formulas for the Factorial Function.

FORMULA

Gamma(x+1) ~ x^x e^(-x) sqrt(2Pi (x+1/6)) Sum_{n>=0} G_n / (x+1/4)^n.

EXAMPLE

G_0 = 1, G_1 = 0, G_2 = 1/144, G_3 = -1/12960.

MAPLE

# See A182912 for G(n).

A182913 := n -> denom(G(n)); seq(A182913(i), i=0..15);

MATHEMATICA

G[n_] := G[n] = Module[{j, J}, J[k_] := J[k] = Module[{j}, If[k == 0, 1, (J[k-1]/k - Sum[J[k-j]*J[j]/(j+1), {j, 1, k-1}])/(1+1/(k+1))]]; Sum[J[2*j]*2^j*6^(j-n)*Gamma[1/2+j]/(Gamma[n-j+1]*Gamma[1/2+j-n]), {j, 0, n}] - Sum[G[j]*(-4)^(j-n)*Gamma[n]/(Gamma[n-j+1]*Gamma[j]), {j, 1, n-1}]]; A182913[n_] := Denominator[G[n]]; Table[A182913[i], {i, 0, 15}] (* Jean-Fran├žois Alcover, Jan 06 2014, translated from Maple *)

CROSSREFS

Cf. A001163, A001164, A182912.

Sequence in context: A231854 A055352 A199406 * A231697 A238932 A230969

Adjacent sequences:  A182910 A182911 A182912 * A182914 A182915 A182916

KEYWORD

nonn,frac

AUTHOR

Peter Luschny, Feb 09 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 28 05:18 EDT 2022. Contains 354903 sequences. (Running on oeis4.)