A391953 Decimal expansion of hypergeom([1/4, 1/2, 3/4], [2/3, 4/3], 1/27)/4.

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

Offset

0,1

Comments

The constant xi = Sum_{k>=0} binomial(L*k+1, k)*A^(-L*k-1)/(L*k+1) is a positive real root of the equation xi^L - A*xi + 1 = 0 where A > 1 and L > 0 (see Exercise n. 1 at p. 188 in Wilf). Here A = L = 4.

Links

Table of n, a(n) for n=0..99.

Herbert S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 188.

Formula

Equals Sum_{k>=0} binomial(4*k+1, k)*4^(-4*k-1)/(4*k+1).

Minimal polynomial: x^4 - 4*x + 1.

Example

0.2509921574904908514198343861632649343605775309...

Mathematica

RealDigits[HypergeometricPFQ[{1/4, 1/2, 3/4}, {2/3, 4/3}, 1/27]/4, 10, 100][[1]]

Crossrefs

Cf. A019819, A094214, A130880, A192918, A382626, A382627.

Sequence in context: A201745 A192042 A388495 * A214119 A088307 A369629

Adjacent sequences: A391950 A391951 A391952 * A391954 A391955 A391956

Keyword

nonn,cons

Author

Stefano Spezia, Dec 23 2025

Status

approved