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 A123180 #21 Feb 16 2025 08:33:02
%S A123180 2,7,1807,10650056950807,
%T A123180 12864938683278671740537145998360961546653259485195807
%N A123180 Even positions of Sylvester's sequence A000058; the denominators of the (greedy) Egyptian fraction expansion of Cahen's constant.
%H A123180 Amiram Eldar, <a href="/A123180/b123180.txt">Table of n, a(n) for n = 0..6</a>
%H A123180 Eugène Cahen, <a href="http://www.numdam.org/item?id=NAM_1891_3_10__508_0">Note sur un développement des quantités numériques, qui présente quelque analogie avec celui en fractions continues</a>, Nouvelles Annales de Mathématiques, Vol. 10 (1891), pp. 508-514.
%H A123180 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CahensConstant.html">Cahen's Constant</a>.
%H A123180 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cahen%27s_constant">Cahen's constant</a>.
%F A123180 a(n) = a(n-1)*(a(n-1)-1)*(a(n-1)*(a(n-1)-1)+1)+1.
%F A123180 a(n) is approximately k^4^n with k = 1.5979102180318731783... (A077125). - _Charles R Greathouse IV_, Dec 12 2013
%F A123180 Sum_{n>=0} 1/a(n) = A118227. - _Amiram Eldar_, Mar 19 2024
%t A123180 f[n_] := n*(n-1)*(n*(n-1)+1)+1; a[0] = 2; a[n_] := a[n] = f[a[n-1]]; Array[a, 5, 0] (* _Amiram Eldar_, Mar 19 2024 *)
%t A123180 1+NestList[#(#+1)(#^2+#+1) &, 1, 4] (* _Oliver Seipel_, Aug 25 2024 *)
%o A123180 (PARI) a(n)=if(n, my(k=a(n-1));k*=k-1; k*(k+1)+1, 2) \\ _Charles R Greathouse IV_, Dec 12 2013
%Y A123180 Cf. A000058, A006279, A006280, A006281, A077125, A118227.
%K A123180 easy,nonn
%O A123180 0,1
%A A123180 _David Eppstein_, Oct 03 2006
%E A123180 a(4) from _Charles R Greathouse IV_, Dec 12 2013