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%I #14 Nov 28 2017 10:52:23
%S 1,0,7,2,7,8,0,6,1,3,3,4,9,1,6,2,2,3,8,7,9,8,2,4,9,5,3,1,0,7,9,4,4,5,
%T 0,4,1,4,5,4,8,6,3,5,3,5,4,0,4,9,8,6,6,8,5,7,5,2,7,8,5,9,0,2,6,2,5,9,
%U 4,3,3,3,1,8,6,1,6,1,7,3,7,5,2,1,5,7,6
%N Decimal expansion of the sum of the reciprocals of the dodecahedral numbers (A006566).
%F Sum_{n>=1} 2/(n(3n-1)(3n-2)) = 1/1 + 1/20 + 1/84 + 1/220 + 1/455 + ... = (sqrt(3)*Pi - 3*log(3))/2.
%e 1.07278061334916223879...
%t RealDigits[Sum[2/(n(3n-1)(3n-2)), {n, 1, Infinity}], 10, 100][[1]]
%o (PARI) (sqrt(3)*Pi - 3*log(3))/2 \\ _Michel Marcus_, Nov 23 2017
%Y Cf. A006566 (dodecahedral numbers).
%Y Sums of inverses: A152623 (tetrahedral numbers), A002117 (cubes), A175577 (octahedral numbers), A175578 (icosahedral numbers).
%K nonn,cons
%O 1,3
%A _Amiram Eldar_, Nov 22 2017
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