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Decimal expansion of Sum_{k>=0} binomial(4*k, 2*k)/2^(6*k).
3

%I #19 Aug 02 2024 13:25:37

%S 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,

%T 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,

%U 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

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

%D Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.49.

%F Equals (1+A020760)*A010503.

%F Equals A020763 + A010503. - _Artur Jasinski_, Dec 20 2020

%F The minimal polynomial is 9*x^4 - 12*x^2 + 1. - _Joerg Arndt_, Sep 20 2023

%F Equals 2F1(1/4,3/4; 1/2; 1/4). - _R. J. Mathar_, Aug 02 2024

%e 1.1153550716504105...

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

%t RealDigits[1/Sqrt[2] + 1/Sqrt[6], 10, 120][[1]] (* _Amiram Eldar_, May 29 2023 *)

%o (PARI) 1/sqrt(6) + 1/sqrt(2) \\ _Michel Marcus_, Jan 15 2021

%Y Cf. A010503, A020760, A020763.

%K cons,easy,nonn

%O 1,4

%A _R. J. Mathar_, Feb 08 2009

%E Typo in definition corrected by _R. J. Mathar_, Feb 09 2009