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

Author

N. J. A. Sloane, Sep 25 2017

Keywords

• sign

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

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