OFFSET
0,1
COMMENTS
Decimal expansion of the alternating sum of the reciprocals of the central binomial coefficients (A000984).
LINKS
Renzo Sprugnoli, Sums of reciprocals of the central binomial coefficients, INTEGERS 6 (2006) #A27
Eric Weisstein's World of Mathematics, Central Binomial Coefficient
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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Ilya Gutkovskiy, Mar 23 2019
STATUS
approved