A145439 Decimal expansion of Sum_{k>=0} binomial(4*k, 2*k)/2^(6*k).

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

Offset

1,4

References

Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, 1996, 4.1.49.

Links

Table of n, a(n) for n=1..93.

Formula

Equals (1+A020760)*A010503.

Equals A020763 + A010503. - Artur Jasinski, Dec 20 2020

The minimal polynomial is 9*x^4 - 12*x^2 + 1. - Joerg Arndt, Sep 20 2023

Equals 2F1(1/4,3/4; 1/2; 1/4). - R. J. Mathar, Aug 02 2024

Equals Product_{k>=1} (1 - (-1)^k/A092259(k)). - Amiram Eldar, Nov 24 2024

Example

1.11535507165041054076705837455583093794582718446458...

Maple

1/2*(1+1/3*3^(1/2))*2^(1/2);

Mathematica

RealDigits[1/Sqrt[2] + 1/Sqrt[6], 10, 120][[1]] (* Amiram Eldar, May 29 2023 *)

Prog

(PARI) 1/sqrt(6) + 1/sqrt(2) \\ Michel Marcus, Jan 15 2021

Crossrefs

Cf. A010503, A020760, A020763, A092259.

Sequence in context: A122277 A198211 A216707 * A165096 A165098 A194584

Adjacent sequences: A145436 A145437 A145438 * A145440 A145441 A145442

Keyword

cons,easy,nonn

Author

R. J. Mathar, Feb 08 2009

Extensions

Typo in definition corrected by R. J. Mathar, Feb 09 2009

Status

approved