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 A054543 #34 Feb 16 2025 08:32:42
%S A054543 2,2,2,4,4,5,5,12,13,41,110,172,248,309,3146,5919,21959,22299,30892,
%T A054543 401838,1719239,30576561,262313756,630913752,3242181301,3250783944,
%U A054543 13827502849,40152067840,137791590233,2514510232695,3217773878849
%N A054543 Engel series expansion (or "Egyptian product") for Catalan's constant G.
%D A054543 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 53-59.
%H A054543 Simon Plouffe, <a href="/A054543/b054543.txt">Table of n, a(n) for n = 1..212</a>
%H A054543 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/catalan/catalan.html">Catalan's Constant</a> [Broken link]
%H A054543 Steven R. Finch, <a href="http://web.archive.org/web/20010603070928/http://www.mathsoft.com/asolve/constant/catalan/catalan.html">Catalan's Constant</a> [From the Wayback machine]
%H A054543 Oleg Marichev, Jonathan Sondow, and Eric W. Weisstein, <a href="https://mathworld.wolfram.com/CatalansConstant.html">Catalan's Constant</a>, MathWorld.
%H A054543 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>
%H A054543 <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%t A054543 EngelExp[A_,n_]:=Join[Array[1&,Floor[A]],First@Transpose@NestList[{Ceiling[1/Expand[ #[[1]]#[[2]]-1]],Expand[ #[[1]]#[[2]]-1]}&,{Ceiling[1/(A-Floor[A])],A-Floor[A]},n-1]]; EngelExp[N[Catalan,7! ],50] (* _Vladimir Joseph Stephan Orlovsky_, Jun 08 2009 *)
%Y A054543 Cf. A006784, A028254, A028257, A006752, A104338, A014538, A153069, A153070, A118323.
%K A054543 nonn
%O A054543 1,1
%A A054543 _Jeppe Stig Nielsen_, Apr 09 2000