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 A384459 #5 May 30 2025 10:35:03
%S A384459 1,6,4,4,0,1,9,5,3,8,9,3,1,6,5,4,2,9,6,5,2,6,3,6,2,1,6,5,0,3,0,2,3,1,
%T A384459 1,4,0,6,4,4,1,3,0,5,1,5,1,9,0,4,1,8,1,5,9,8,1,6,6,2,1,1,5,9,4,3,8,9,
%U A384459 1,7,3,1,0,0,7,1,4,2,1,2,7,6,4,9,2,3,1,6,3,5,1,5,5,1,5,7,6,5,5,9,4,4,8,6,0
%N A384459 Decimal expansion of Sum_{k>=1} (-1)^k*(3*k+1)*H(k)^3/2^k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.
%D A384459 K. Ramachandra and R. Sitaramachandrarao, On series, integrals and continued fractions - II, Madras Univ. J., Sect. B, 51 (1988), pp. 181-198.
%H A384459 K. Ramachandra, <a href="https://doi.org/10.46298/hrj.1981.93">On series integrals and continued fractions I</a>, Hardy-Ramanujan Journal, Vol. 4 (1981), pp. 1-11.
%H A384459 K. Ramachandra, <a href="https://doi.org/10.4064/aa99-3-3">On series, integrals and continued fractions, III</a>, Acta Arithmetica, Vol. 99, No. 3 (2001), pp. 257-266.
%H A384459 Michael Ian Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's Catalog of the Real Numbers</a>, 2011, p. 225.
%F A384459 Equals A016578^2 = log(3/2)^2 (Ramachandra, 1981).
%F A384459 Equals Sum_{k>=1} (-1)^(k+1)*H(k)/((k+1)*2^k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number (Shamos, 2011).
%e A384459 0.16440195389316542965263621650302311406441305151904...
%t A384459 RealDigits[Log[3/2]^2, 10, 120][[1]]
%o A384459 (PARI) log(3/2)^2
%Y A384459 Cf. A001008, A002805, A016578.
%Y A384459 Related constants: A152648, A152649, A152651, A218505, A233090, A238168, A238181, A238182, A241753, A244667, A253191, A256988, A345203.
%K A384459 nonn,cons,easy
%O A384459 0,2
%A A384459 _Amiram Eldar_, May 30 2025