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 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 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-François 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

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Last modified September 20 22:20 EDT 2018. Contains 315247 sequences. (Running on oeis4.)