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%I #27 Jun 21 2023 06:37:38
%S 8,1,7,7,6,6,1,6,6,7,1,9,3,4,3,7,1,3,0,0,6,7,8,5,4,5,7,4,9,8,1,1,8,8,
%T 1,6,9,0,6,0,0,1,6,1,2,3,2,3,0,6,3,0,4,9,4,4,8,1,6,0,1,1,3,9,2,0,7,2,
%U 3,4,6,3,6,3,6,3,3,6,5,8,7,2,7,0,3,5,9,9,2,3,9,5,7
%N Decimal expansion of Sum_{n>=1} (-1)^(n+1)*6/(n*(n+1)*(n+2)).
%C The sum of the reciprocals of binomial(n,3) for n >= 3 (or A000292(n), for n >= 1) with alternating signs.
%C Also see A242023.
%F Equals 12*log(2) - 15/2.
%e 0.8177661667193437130067854...
%t RealDigits[Chop[Sum[N[(-1)^(n+1)*6/(n*(n+1)*(n+2)),150],{n,1,Infinity}]], 10,120][[1]] (* _Harvey P. Dale_, Jun 02 2016 *)
%t RealDigits[12*Log[2] - 15/2, 10, 120][[1]] (* _Amiram Eldar_, Jun 20 2023 *)
%o (PARI) 12*log(2) - 15/2 \\ _Michel Marcus_, Aug 13 2014
%o (PARI) sumalt(n=1, (-1)^(n + 1)*6/(n*(n + 1)*(n + 2))) \\ _Michel Marcus_, Aug 14 2014
%Y Cf. A242023, A000217, A000292, A000332, A002162.
%K nonn,cons
%O 0,1
%A _Richard R. Forberg_, Aug 11 2014
%E Prior Mathematica program replaced by _Harvey P. Dale_, Jun 02 2016
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