cp's OEIS Frontend

A244646 Decimal expansion of the sum of the reciprocals of the 9-gonal (or enneagonal or nonagonal) numbers (A001106).

%I A244646 #29 Apr 22 2024 07:28:54
%S A244646 1,2,4,3,3,2,0,9,2,6,1,5,3,7,1,2,9,8,9,2,0,6,6,0,7,7,3,9,6,3,1,0,1,4,
%T A244646 2,8,2,1,3,5,8,4,4,1,0,1,0,3,0,0,9,9,6,2,4,4,1,5,2,8,1,7,5,2,5,3,8,6,
%U A244646 6,0,7,4,3,8,4,4,0,8,5,1,9,7,8,6,9,0,0,1,3,2,3,2,5,8,8,3,2,8,6,0,0,7,3,6,8
%N A244646 Decimal expansion of the sum of the reciprocals of the 9-gonal (or enneagonal or nonagonal) numbers (A001106).
%H A244646 Vincenzo Librandi, <a href="/A244646/b244646.txt">Table of n, a(n) for n = 1..1000</a>
%H A244646 Ravi P. Agarwal, <a href="https://doi.org/10.4236/jamp.2021.98132">Pythagoreans Figurative Numbers: The Beginning of Number Theory and Summation of Series</a>, Journal of Applied Mathematics and Physics, Vol.9,  No.8 (2021), pp. 2038-2113. See p. 2076.
%H A244646 Wikipedia, <a href="http://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>.
%F A244646 Equals Sum_{n>=1} 2/(7n^2 - 5n).
%F A244646 Equals (2*log(14) + 4*(cos(Pi/7)*log(cos(3*Pi/14)) + log(sin(Pi/7))*sin(Pi/14) - log(cos(Pi/14)) * sin(3*Pi/14)) + Pi*tan(3*Pi/14))/5. - _Vaclav Kotesovec_, Jul 04 2014
%F A244646 Equals 14/25 - (2/5)*(gamma + psi(-5/7)), where gamma is Euler's constant (A001620) and psi(x) is the digamma function (Agarwal, 2021), psi(-5/7) = psi(2/7)+7/5 = -2.285517..., see A354628. - _Amiram Eldar_, Nov 12 2021
%e A244646 1.2433209261537129892066077396310142821358441010300996244152817525...
%t A244646 RealDigits[ Sum[2/(7n^2 - 5n), {n, 1 , Infinity}], 10, 111][[1]]
%Y A244646 Cf. A000038, A001106, A013661, A001620, A244639, A244644, A244645, A244647, A244648, A244649.
%K A244646 nonn,cons,easy
%O A244646 1,2
%A A244646 _Robert G. Wilson v_, Jul 03 2014