This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A152648 #53 Dec 12 2024 15:12:04
%S A152648 2,4,0,4,1,1,3,8,0,6,3,1,9,1,8,8,5,7,0,7,9,9,4,7,6,3,2,3,0,2,2,8,9,9,
%T A152648 9,8,1,5,2,9,9,7,2,5,8,4,6,8,0,9,9,7,7,6,3,5,8,4,5,4,3,1,1,0,6,8,3,6,
%U A152648 7,6,4,1,1,5,7,2,6,2,6,1,8,0,3,7,2,9,1,1,7,4,7,2,1,8,6,7,0,5,1,6,2,9,2,3,9
%N A152648 Decimal expansion of 2*zeta(3).
%C A152648 A division by 2 is missing in Mezo's penultimate formula on page 4.
%C A152648 This constant is irrational but not known to be transcendental. - _Charles R Greathouse IV_, Sep 02 2024
%D A152648 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3, p. 43.
%H A152648 Harry J. Smith, <a href="/A152648/b152648.txt">Table of n, a(n) for n = 1..20000</a>
%H A152648 Ilham A. Aliev and Ayhan Dil, <a href="https://arxiv.org/abs/2008.02488">Tornheim-like series, harmonic numbers and zeta values</a>, arXiv:2008.02488 [math.NT], 2020, p. 2.
%H A152648 R. Barbieri, J. A. Mignaco, and E. Remiddi, <a href="https://dx.doi.org/10.1007/BF02728545">Electron form factors up to fourth order. I.</a>, Il Nuovo Cim. 11A (4) (1972) 824-864, Table II. (3).
%H A152648 David Borwein and J. M. Borwein, <a href="https://doi.org/10.1090/S0002-9939-1995-1231029-X">On an intriguing integral and some series related to zeta(4)</a>, Proc. Am. Math. Soc. 123 (1995) 1191-1198.
%H A152648 Istvan Mezo, <a href="http://arxiv.org/abs/0811.0042">Summation of Hyperharmonic Numbers</a>, arXiv:0811.0042 [math.CO], 2008.
%H A152648 Michael Penn, <a href="https://www.youtube.com/watch?v=5KpGSMyUANU">a nice double sum.</a>, YouTube video, 2020.
%H A152648 Michael Penn, <a href="https://www.youtube.com/watch?v=5OPLW8wH_Po">Euler's harmonic number identity</a>, YouTube video, 2020.
%F A152648 Equals 2*A002117 = Sum_{j>=1} H(j)/j^2 where H(j) = A001008(j)/A002805(j).
%F A152648 Equals Integral_{x>=0} x^2/(exp(x)-1). - _Jean-François Alcover_, Nov 12 2013
%F A152648 Equals Sum_{m>=1} Sum_{n>=1} 1/(m*n*(m + n)). - _Jean-François Alcover_, Jun 17 2020
%F A152648 Equals Integral_{x=0..1} log(x)^2/(1-x) dx. - _Amiram Eldar_, Aug 03 2020
%F A152648 Equals the absolute value of psi''(1) = -2.404..., the 2nd derivative of the digamma function at 1. - _R. J. Mathar_, Aug 29 2023
%e A152648 Equals 2.4041138063191885707994...
%t A152648 RealDigits[2*Zeta[3],10,120][[1]] (* _Harvey P. Dale_, Dec 02 2011 *)
%o A152648 (PARI) default(realprecision, 20080); x=2*zeta(3); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b152648.txt", n, " ", d)); \\ _Harry J. Smith_, Jul 12 2009
%Y A152648 Cf. A002117, A001008, A002805.
%Y A152648 Cf. A060804 (continued fraction).
%K A152648 cons,easy,nonn
%O A152648 1,1
%A A152648 _R. J. Mathar_, Dec 10 2008