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A307086
Decimal expansion of 4*(5 - sqrt(5)*log(phi))/25, where phi is the golden ratio (A001622).
0
6, 2, 7, 8, 3, 6, 4, 2, 3, 6, 1, 4, 3, 9, 8, 3, 8, 4, 4, 4, 4, 2, 2, 6, 7, 0, 6, 8, 1, 9, 7, 5, 7, 8, 2, 9, 8, 3, 0, 1, 7, 1, 7, 2, 6, 9, 8, 3, 8, 8, 4, 1, 3, 8, 0, 9, 7, 1, 9, 7, 5, 5, 8, 4, 0, 2, 9, 7, 5, 5, 1, 3, 8, 1, 5, 5, 4, 7, 2, 1, 5, 4, 5, 5, 4, 0, 3, 8, 9, 4, 1, 2, 1, 1, 1, 2, 0, 1, 7, 8, 3, 7, 4, 6, 7, 7, 8, 2, 8, 8, 6, 7, 0, 2, 9, 3, 8, 5, 7, 4
OFFSET
0,1
COMMENTS
Decimal expansion of the alternating sum of the reciprocals of the central binomial coefficients (A000984).
FORMULA
Equals Sum_{k>=0} (-1)^k/binomial(2*k,k).
Equals Sum_{k>=0} (-1)^k*(k!)^2/(2*k)!.
EXAMPLE
1/1 - 1/2 + 1/6 - 1/20 + 1/70 - 1/252 + ... = 0.62783642361439838444422670681975782983017172698388...
MATHEMATICA
RealDigits[4 (5 - Sqrt[5] Log[GoldenRatio])/25, 10, 120][[1]]
PROG
(PARI) 4*(5 - sqrt(5)*log((sqrt(5)+1)/2))/25 \\ Charles R Greathouse IV, May 15 2019
KEYWORD
nonn,cons
AUTHOR
Ilya Gutkovskiy, Mar 23 2019
STATUS
approved