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 A195055 #69 Apr 10 2025 19:31:31
%S A195055 3,2,8,9,8,6,8,1,3,3,6,9,6,4,5,2,8,7,2,9,4,4,8,3,0,3,3,3,2,9,2,0,5,0,
%T A195055 3,7,8,4,3,7,8,9,9,8,0,2,4,1,3,5,9,6,8,7,5,4,7,1,1,1,6,4,5,8,7,4,0,0,
%U A195055 1,4,9,4,0,8,0,6,4,0,1,7,4,7,6,6,7,2,5,7,8,0,1,2,3,9,5,1,7,4,1,0,6,0,8,0,0
%N A195055 Decimal expansion of Pi^2/3.
%D A195055 Marc Briane and Gilles Pagès, Théorie de l'Intégration, Vuibert, 2004, 3ème édition, exercice 12.15, p. 256.
%H A195055 George E. Andrews, <a href="https://doi.org/10.1073/pnas.0500218102">Partitions with short sequences and mock theta functions</a>, Proceedings of the National Academy of Sciences, Vol. 102, No. 13 (2005), pp. 4666-4671.
%H A195055 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A195055 Equals 3 + A145426.
%F A195055 Equals -Sum_{n>=1} Psi_2(n), where Psi_2 is the tetragamma function. - _Istvan Mezo_, Oct 25 2012
%F A195055 Equals Integral_{x=0..1} (log(x)/(x - 1))^2 dx. - _Jean-François Alcover_, Mar 21 2013
%F A195055 Equals Integral_{x=-oo..oo} x^2/sinh(x)^2 dx. - _Amiram Eldar_, Aug 06 2020
%F A195055 Equals Integral_{x=0..oo} (log(x+1)/x)^2 dx (reference Briane and Pagès). - _Bernard Schott_, Feb 13 2022
%F A195055 Equals Sum_{n>=1} H(n) * binomial(2*n, n) / (n * 4^n), where H(n) is the n-th harmonic number. - _Antonio Graciá Llorente_, Apr 04 2025
%e A195055 3.289868133696452872944830333292050378438...
%t A195055 RealDigits[Pi^2/3, 10, 105][[1]] (* _T. D. Noe_, Oct 05 2011 *)
%o A195055 (Magma) pi:=Pi(RealField(110)); Reverse(Intseq(Floor(10^105*pi^2/3))); // _Vincenzo Librandi_, Jan 12 2016
%o A195055 (PARI) 2*zeta(2) \\ _Charles R Greathouse IV_, Jan 20 2022
%o A195055 (PARI) sumnumrat(1/x^2,-oo) \\ _Charles R Greathouse IV_, Jan 20 2022
%Y A195055 Cf. A002388, A102753, A091476, 2*A013661, A164102.
%Y A195055 Cf. A024916 (partial sums of A000203).
%Y A195055 Cf. A001008/A002805, A145426.
%K A195055 nonn,cons
%O A195055 1,1
%A A195055 _Omar E. Pol_, Oct 04 2011
%E A195055 Extended by _T. D. Noe_, Oct 05 2011