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A244648 Decimal expansion of the sum of the reciprocals of the hendecagonal numbers (A051682).

%I A244648 #10 Feb 08 2023 23:03:54
%S A244648 1,1,9,5,4,3,4,1,1,6,5,2,9,6,2,7,9,7,4,3,5,2,4,9,9,2,3,4,6,9,8,4,9,9,
%T A244648 3,5,4,8,8,4,6,8,2,6,2,7,0,8,4,6,5,8,0,6,2,3,8,6,0,2,1,6,0,3,0,1,7,3,
%U A244648 5,8,4,7,3,3,7,0,3,1,7,6,0,1,4,6,4,4,8,4,1,7,5,4,8,5,5,1,1,2,3,1,8,5,5,4,7
%N A244648 Decimal expansion of the sum of the reciprocals of the hendecagonal numbers (A051682).
%H A244648 Wikipedia, <a href="http://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>
%F A244648 Sum_{n=1..infinity} 2/(9n^2 - 7n).
%F A244648 Equals (5*log(3) + Pi*cot(2*Pi/9) - 4*cos(2*Pi/9)*log(cos(Pi/18)) + 4*cos(Pi/9)*log(sin(2*Pi/9)) - 4*log(sin(Pi/9))*sin(Pi/18))/7. - _Vaclav Kotesovec_, Jul 04 2014
%e A244648 1.195434116529627974352499234698499354884682627084658062386021603017...
%t A244648 RealDigits[ Sum[2/(9n^2 - 7n), {n, 1 , Infinity}], 10, 111][[1]]
%Y A244648 Cf. A000038, A013661, A244639, A244644, A244645, A244646, A244647, A244649.
%K A244648 nonn,cons,easy
%O A244648 1,3
%A A244648 _Robert G. Wilson v_, Jul 03 2014