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 A091154 #11 Feb 16 2025 08:32:52 %S A091154 1,1,-1,1,-5,7,-21,11,-429,715,-2431,4199,-29393,52003,-185725,334305, %T A091154 -3231615,3535767,-64822395,39803225,-883631595,1641030105,-407771117, %U A091154 11435320455,-171529806825,107492012277,-1215486600363,2295919134019 %N A091154 Numerator of Maclaurin expansion of (t*sqrt(t^2+1) + arcsinh(t))/2, the arc length of Archimedes' spiral. %C A091154 From _Mikhail Gaichenkov_, Feb 05 2013: (Start) %C A091154 For Archimedean spiral (r=at) and the arc length s(t)= a(t*sqrt(t^2+1) + arcsinh(t))/2, the limit of s’’(t)=a, t- -> infinity. In other words, a point moves with uniform acceleration along the spiral while the spiral corresponds to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. %C A091154 The error of approximation for large t: |a-s’’(t)| ~ a/(2(1+t^2)) (Gaichenkov private research). %C A091154 The arc of the Archimedean spiral is approximated by the differential equation in polar coordinates r’^2+r^2=(at)^2 (see A202407). (End) %H A091154 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ArchimedesSpiral.html">Archimedes' Spiral</a> %e A091154 t + t^3/6 - t^5/40 + t^7/112 - (5*t^9)/1152 + (7*t^11)/2816 - ... %Y A091154 Denominators are in A002595. %K A091154 sign,easy %O A091154 1,5 %A A091154 _Eric W. Weisstein_, Dec 22 2003