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 A057438 #17 Mar 09 2023 17:31:49
%S A057438 1,1,2,5,27,739,546391,298543324411,89128116550480609893151,
%T A057438 7943821159836055611643954282977557048699079331,
%U A057438 63104294619459055797454850600852928915607093463575707111291209057699988334565551829102647591
%N A057438 a(1) = 1; a(n+1) = (Product_{k = 1..n} [a(k)]) * (Sum_{j = 1..n} [1/a(j)]).
%F A057438 a(n) = a(n-1)^2+a(n-1)a(n-2)-a(n-2)^3 (valid for all n>3). - _Ivan Sadofschi_, Feb 22 2011
%F A057438 a(n) = a(n-1)^2+A074056(n-2) where A074056 is partial product of A057438. Close to a(n-1)^2+a(n-1)*0.365177806085453... and 1.1087260396143829635274191...^(2^n). - _Henry Bottomley_, Aug 14 2002
%e A057438 a(5) = a(1)*a(2)*a(3)*a(4)*(1/a(1) + 1/a(2) + 1/a(3) + 1/a(4)) = 1*1*2*5*(1 + 1 + 1/2 + 1/5) = 27.
%t A057438 a[1] = 1; a[n_] := a[n] = Sum[1/a[n - k], {k, n - 1}] Product[a[n - k], {k, n - 1}]; Table[ a[n], {n, 11}] (* _Robert G. Wilson v_, Jun 14 2005 *)
%Y A057438 Cf. A074046, A074056, A108176.
%K A057438 easy,nonn
%O A057438 1,3
%A A057438 _Leroy Quet_, Sep 08 2000
%E A057438 More terms from _Leroy Quet_, Sep 08 2000