A292753 Numerators of coefficients in an asymptotic expansion of the Wallis sequence in inverse powers of n+5/8.
1, -1, 0, 3, 3, -51, -75, 2253, 1491, -192651, -187275, 27071553, 278562603, -5649998901, -36187521825, 1637735135403, 25110810761403, -628821435060051, -1403714584628625, 308746181051792553, 6294348598730683953, -188636884672112018601, -2161564244998001617125
Offset: 0
Keywords
References
- Chao-Ping Chen, Richard B. Paris, On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas, Applied Mathematics and Computation 293 (2017) 30-39. See (3.1).
Links
- Chao-Ping Chen, Richard B. Paris, On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas, arXiv:1511.09217 [math.CA], 2015. See (3.1).
- N. Elezovic, L. Lin, L. Vukšic, Inequalities and asymptotic expansions for the Wallis sequence and the sum of the Wallis ratio, J. Math. Inequal. 7 (2013) 679-695. See p. 687.
Crossrefs
Cf. A292754.
Programs
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Mathematica
Numerator[CoefficientList[Series[Gamma[n + 3/8]^2 / (2*Gamma[n - 1/8] * Gamma[n + 7/8]), {n, Infinity, 25}], 1/n]] (* Vaclav Kotesovec, Jun 02 2019 *)
Extensions
a(2)=0 inserted by Michel Marcus, Jun 02 2019
More terms from Vaclav Kotesovec, Jun 02 2019