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A373508
Decimal expansion of sqrt(3)*Pi/6 + Pi^2/36 - 1.
1
1, 8, 1, 0, 5, 5, 3, 5, 9, 9, 2, 5, 1, 4, 6, 6, 6, 4, 7, 0, 9, 1, 0, 8, 3, 2, 3, 2, 6, 2, 0, 8, 2, 0, 6, 4, 3, 4, 5, 1, 9, 1, 4, 4, 0, 9, 1, 4, 1, 7, 0, 0, 2, 7, 4, 0, 7, 5, 3, 5, 5, 0, 5, 9, 2, 2, 3, 9, 6, 1, 6, 8, 9, 6, 3, 7, 1, 0, 4, 2, 0, 8, 1, 4
OFFSET
0,2
FORMULA
Equals Sum_{n>=2} 1/((n-1)^2*binomial(2n,n)).
Sum_{n>=2} (-1)^n/((n-1)^2*binomial(2n,n)) = 1 - sqrt(5)*log(phi) + log(phi)^2 = 0.1555... where phi is the golden ratio.
Equals A093766 + A100044/4 - 1. - Stefano Spezia, Jun 07 2024
EXAMPLE
0.181055359925146664709108323262082...
MAPLE
(sqrt(3)+Pi/6)*Pi/6-1; evalf(%) ;
MATHEMATICA
RealDigits[Sqrt[3]*Pi/6 + Pi^2/36 - 1, 10, 120][[1]] (* Amiram Eldar, Jun 10 2024 *)
PROG
(PARI) sqrt(3)*Pi/6 + Pi^2/36 - 1 \\ Amiram Eldar, Jun 10 2024
CROSSREFS
Cf. A093766, A100044, A373507 (denominator n-1), A073010 (denominator n).
Sequence in context: A351129 A214097 A357468 * A194732 A217739 A110544
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Jun 07 2024
STATUS
approved