cp's OEIS Frontend

A295421 Decimal expansion of the sum of the reciprocals of the dodecahedral numbers (A006566).

%I A295421 #14 Nov 28 2017 10:52:23
%S A295421 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 A295421 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 A295421 4,3,3,3,1,8,6,1,6,1,7,3,7,5,2,1,5,7,6
%N A295421 Decimal expansion of the sum of the reciprocals of the dodecahedral numbers (A006566).
%F A295421 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 A295421 1.07278061334916223879...
%t A295421 RealDigits[Sum[2/(n(3n-1)(3n-2)), {n, 1, Infinity}], 10, 100][[1]]
%o A295421 (PARI) (sqrt(3)*Pi - 3*log(3))/2 \\ _Michel Marcus_, Nov 23 2017
%Y A295421 Cf. A006566 (dodecahedral numbers).
%Y A295421 Sums of inverses: A152623 (tetrahedral numbers), A002117 (cubes), A175577 (octahedral numbers), A175578 (icosahedral numbers).
%K A295421 nonn,cons
%O A295421 1,3
%A A295421 _Amiram Eldar_, Nov 22 2017