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 A057268 #13 Feb 13 2025 10:01:19
%S A057268 1,3,6,18,216,42768,1819863936,3311826913612597248,
%T A057268 10968197499701667312529793029329125376,
%U A057268 120301356392461906290006219878693096559247086148184247242087281541542576128
%N A057268 a(n-1)+k=a(n) => a(n)*k=a(n+1).
%C A057268 For +k and ^k see A057269. (Using *k and ^k gives another formulation of A014222. In this case the sequence could start 1,2 - see A014221.)
%C A057268 See the Comments section in A001696 as a connection to some sieving process. - _Ctibor O. Zizka_, Feb 13 2025
%F A057268 a(0) = 1, a(1) = 3, for n >= 2, a(n) = a(n - 1)*(a(n - 1) - a(n - 2)). - _Ctibor O. Zizka_, Feb 13 2025
%t A057268 nxt[{a_,b_}]:={b,b(b-a)}; NestList[nxt,{1,3},9][[All,1]] (* _Harvey P. Dale_, Sep 05 2017 *)
%Y A057268 Cf. A001696, A057269.
%K A057268 easy,nonn
%O A057268 0,2
%A A057268 _Jonas Wallgren_, Aug 22 2000
%E A057268 More terms from _Harvey P. Dale_, Sep 05 2017