A338856 Decimal expansion of Sum_{k>=0} binomial(4*k,2*k)^2 / (2^(8*k) * (2*k + 1)).

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

Offset

1,3

References

Pablo Fernandez Refolio, Problem 12180, The American Mathematical Monthly 127, April 2020, p. 373.

Links

Table of n, a(n) for n=1..105.

Formula

Equals 2/Pi + sqrt(Pi/2) / Gamma(3/4)^2 - sqrt(2) * Gamma(3/4)^2 / Pi^(3/2).

Equals hypergeom([1/4, 1/4, 3/4, 3/4], [1/2, 1, 3/2], 1).

Example

1.0898667322907479353258017958072963604855169777781363398319609472070578367683...

Maple

evalf(2/Pi + sqrt(Pi/2) / GAMMA(3/4)^2 - sqrt(2) * GAMMA(3/4)^2 / Pi^(3/2), 120);

Mathematica

RealDigits[2/Pi + Sqrt[Pi/2]/Gamma[3/4]^2 - Sqrt[2]*Gamma[3/4]^2/Pi^(3/2), 10, 100][[1]]
N[HypergeometricPFQ[{1/4, 1/4, 3/4, 3/4}, {1/2, 1, 3/2}, 1], 120]

Crossrefs

Cf. A068465, A276483.

Sequence in context: A374813 A265296 A230154 * A182999 A356532 A019873

Adjacent sequences: A338853 A338854 A338855 * A338857 A338858 A338859

Keyword

nonn,cons

Author

Vaclav Kotesovec, Nov 12 2020

Status

approved