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.
a=1;b=2;lst={a,b};Do[c=2*a*b-a;AppendTo[lst,c];a=b;b=c,{n,11}];lst
RecurrenceTable[{a[1]==1,a[2]==2,a[n]==2a[n-2]a[n-1]-a[n-2]},a,{n,15}] (* Harvey P. Dale, Sep 10 2016 *)
a=1;b=2;lst={a,b};Do[c=2*a*b-b;AppendTo[lst,c];a=b;b=c,{n,12}];lst
RecurrenceTable[{a[1]==1,a[2]==2,a[n]==2a[n-2]a[n-1]-a[n-1]},a,{n,14}] (* Harvey P. Dale, Jan 27 2012 *)
a=1;b=3;lst={a,b};Do[c=2*a*b-a-b;AppendTo[lst,c];a=b;b=c,{n,12}];lst
nxt[{a_,b_}]:={b,2*a*b-a-b}; NestList[nxt,{1,3},12][[All,1]] (* Harvey P. Dale, Jan 03 2022 *)
a(3) = a(1) * a(2) - (a(1) + a(2)) = 2 * 5 - (2 + 5) = 3.
I:=[2,5]; [n le 2 select I[n] else Self(n-1)*Self(n-2)-(Self(n-1)+Self(n-2)): n in [1..14]]; // Vincenzo Librandi, Jul 10 2019
RecurrenceTable[{x[n+1]==x[n]*x[n-1]-(x[n]+x[n-1]),x[1]==2,x[2]==5},x,{n,1,18}]
a=2;b=2;lst={a,b};Do[c=2*a*b-a-b;AppendTo[lst,c];a=b;b=c,{n,12}];lst