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 A085644 #11 Mar 14 2023 19:16:35
%S A085644 1,1,5,25,157,1265,12661,151945,2127245,34035937,612646885,
%T A085644 12252937721,269564629885,6469551117265,168208329048917,
%U A085644 4709833213369705,141294996401091181,4521439884834917825,153728956084387206085,5534242419037939419097,210301211923441697925725
%N A085644 a(0) = 1; a(n+1) = a(n)*2n + 2n + 1.
%C A085644 Sum of reciprocals = 2.2472460058071954531775930749...
%p A085644 a:= proc(n) option remember;
%p A085644 `if`(n=0, 1, 2*((n-1)*a(n-1)+n)-1)
%p A085644 end:
%p A085644 seq(a(n), n=0..20); # _Alois P. Heinz_, Mar 14 2023
%t A085644 nxt[{n_,a_}]:={n+1,a*2n+2n+1}; Transpose[NestList[nxt,{1,1},20]][[2]] (* _Harvey P. Dale_, Aug 06 2016 *)
%o A085644 (PARI) sum2x(n) = { s=1; sr=0; forstep(x=2,n,2, s=x*(s+1)+1; print1(s","); sr += 1.0/s; ); print(); print(sr) }
%Y A085644 a(n) = 2 * A010844(n-1) - 1 = A007566(n-1) - 2n - 2 for n>=1.
%K A085644 nonn,easy
%O A085644 0,3
%A A085644 _Cino Hilliard_, Aug 19 2003
%E A085644 a(0)=1 prepended and edited by _Alois P. Heinz_, Mar 14 2023