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 A092053 #18 Aug 14 2021 15:33:52
%S A092053 1,1,7,19,53,81,823,5359,12923,21877,102061,354883,808865,1433689,
%T A092053 25699639,369784999,817787423,1487830821,6512750579,23917578595,
%U A092053 51908057021,96040578001,827937066989,6166467806391,13211837015707
%N A092053 Denominators of the convergents of the continued fraction expansion [1;1/2,1/3,1/4,...,1/n,...].
%C A092053 Numerators of convergents are A001902 (successive denominators of Wallis's product approximation to Pi/2). Sum of numerators and denominators equals powers of 2: A001902(n) + a(n) = 2^A092054(n).
%H A092053 Robert Israel, <a href="/A092053/b092053.txt">Table of n, a(n) for n = 1..1663</a>
%F A092053 a(n) = 2^A092054(n) - A001902(n).
%p A092053 R:= gfun:-rectoproc({r(n) = (r(n - 1))/(n - 1) + r(n - 2), r(1) = 0, r(2) = 1}, r(n), remember):
%p A092053 seq(numer(R(n)),n=2..30); # _Robert Israel_, May 14 2017
%t A092053 Numerator[RecurrenceTable[{r[n] == (r[n - 1])/(n - 1) + r[n - 2], r[1] == 0, r[2] == 1}, r, {n, 2, 30}]] (* _Terry D. Grant_, May 07 2017, fixed by _Vaclav Kotesovec_, Aug 14 2021 *)
%t A092053 Table[Numerator[ContinuedFractionK[1, 1/k , {k, 1, n}]], {n, 1, 30}] (* _Vaclav Kotesovec_, Aug 14 2021 *)
%o A092053 (PARI) a(n)=local(A);CF=contfracpnqn(vector(n,k,1/k));A=denominator(CF[1,1]/CF[2,1])
%Y A092053 Cf. A001902, A092054.
%K A092053 frac,nonn
%O A092053 1,3
%A A092053 _Paul D. Hanna_, Feb 19 2004