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 A257134 #31 Jun 18 2025 18:06:08
%S A257134 2,1,6,4,6,4,6,4,6,7,4,2,2,2,7,6,3,8,3,0,3,2,0,0,7,3,9,3,0,8,2,3,3,5,
%T A257134 8,0,5,5,4,9,5,0,1,9,0,3,8,3,7,4,5,3,8,1,5,3,6,5,9,5,2,4,3,0,8,8,8,2,
%U A257134 4,1,2,3,2,3,7,3,9,3,7,6,9,3,1,1,3,8,1,9,2,7,1,8,8,3,3,9,9,8,3,4,4,6,5,9,8
%N A257134 Decimal expansion of Pi^4/45.
%D A257134 L. J. P. Kilford, Modular Forms: A Classical and Computational Introduction, Imperial College Press, 2008, p. 15.
%H A257134 Alain Tissier, <a href="http://www.jstor.org/stable/2589763">Apéry's Constant</a>, Solution to Problem 10635, The American Mathematical Monthly, Vol. 106, No. 10 (1999), pp. 965-966.
%H A257134 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EisensteinSeries.html">Eisenstein Series</a>.
%H A257134 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A257134 Pi^4/45 = 2*zeta(4) = G_4(oo), where the function G_k(z) is the Eisenstein nonzero modular form of weight k.
%F A257134 Equals -Integral_{x=0..1} log(x)^2 * log(1 - x)/x dx. - _Amiram Eldar_, Jul 21 2020
%F A257134 Equals Sum_{n,m>=1} (Pi^2/6 - Sum_{k=1..n+m} 1/k^2)/(n*m) (Tissier, 1999). - _Amiram Eldar_, Jan 27 2024
%F A257134 Equals Integral_{x=0..1} Li(3,sqrt(x))/x dx, where Li(n,x) is the polylogarithm function. - _Kritsada Moomuang_, Jun 18 2025
%F A257134 Equals 2*A013662 = A231535/3. - _Hugo Pfoertner_, Jun 18 2025
%e A257134 2.16464646742227638303200739308233580554950190383745381536595243...
%t A257134 RealDigits[Pi^4/45, 10, 105] // First
%o A257134 (PARI) Pi^4/45 \\ _Charles R Greathouse IV_, Oct 01 2022
%Y A257134 Cf. A013662, A092425, A231535, A257136.
%K A257134 nonn,cons,easy
%O A257134 1,1
%A A257134 _Jean-François Alcover_, Apr 16 2015