A359533 Decimal expansion of Sum_{k>=0} (-1/64)^k*binomial(2*k, k)^3*(4*k + 1)*H_k, where H_k is the k-th harmonic number (negated).

2, 7, 6, 4, 2, 7, 2, 0, 4, 2, 4, 5, 9, 8, 6, 5, 7, 3, 0, 9, 2, 6, 3, 9, 8, 2, 5, 6, 1, 6, 8, 8, 9, 9, 4, 6, 7, 8, 3, 7, 4, 0, 7, 9, 5, 1, 9, 0, 4, 8, 5, 0, 6, 3, 0, 3, 2, 7, 7, 6, 9, 2, 0, 2, 7, 0, 3, 3, 7, 9, 6, 9, 4, 4, 5, 8, 9, 8, 7, 9, 7, 1, 0, 9, 8, 0, 1

Offset: 0

Author

Stefano Spezia, Jan 04 2023

Keywords

• nonn
• cons

Examples

			0.276427204245986573092639825616889946783740795...
		

Links

• John M. Campbell, Applications of a class of transformations of complex sequences, arXiv:2212.13305 [math.NT], 2022. See p. 6.

Crossrefs

Cf. A000796, A001008, A002805, A002897, A016639, A016813, A063448, A068465, A068466, A091925, A203142, A203143.

Cf. A359532.

Programs

Mathematica

First[RealDigits[N[(Gamma[1/8]Gamma[3/8]/(Gamma[1/4]Gamma[3/4]))^2/(6Sqrt[2]Pi)-4Log[2]/Pi,100]]]

Formula

Equals 4*log(2)/Pi - (Gamma(1/8)*Gamma(3/8)/(Gamma(1/4)*Gamma(3/4)))^2/(6*sqrt(2)*Pi).

Equals 4*log(2)/Pi - (Gamma(1/8)*Gamma(3/8))^2/(12*sqrt(2)*Pi^3).