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 A121688 #16 Mar 15 2021 21:30:21
%S A121688 1,2,3,6,15,49,210,1191,8981,90405,1219297,22105506,540476679,
%T A121688 17875316557,802011318369,48947781204529,4073596070782653,
%U A121688 463360670014324153,72183972733773232361,15430254274957714069057
%N A121688 G.f.: Sum_{n>=0} x^n * (1+x)^(2^n).
%H A121688 Vaclav Kotesovec, <a href="/A121688/b121688.txt">Table of n, a(n) for n = 0..100</a>
%F A121688 a(n) = Sum_{k=0..n} C(2^k,n-k).
%F A121688 Lim_{n->infinity} a(n)^(1/n^2) = 2^(1/4). - _Vaclav Kotesovec_, Oct 05 2020
%F A121688 G.f.: Sum_{n>=0} ( log(1 + x)^n / n! ) / (1 - 2^n*x). - _Paul D. Hanna_, Jan 23 2021
%p A121688 A121688:= n-> add(binomial(2^k,n-k), k=0..n); seq(A121688(n), n=0..20); # _G. C. Greubel_, Mar 15 2021
%t A121688 Table[Sum[Binomial[2^k,n-k], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Oct 05 2020 *)
%o A121688 (PARI) a(n)=sum(k=0,n,binomial(2^k,n-k))
%o A121688 (Sage) [sum(binomial(2^k, n-k) for k in (0..n)) for n in (0..20)] # _G. C. Greubel_, Mar 15 2021
%o A121688 (Magma) [(&+[Binomial(2^k, n-k): k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Mar 15 2021
%Y A121688 Cf. A136501.
%K A121688 nonn
%O A121688 0,2
%A A121688 _Paul D. Hanna_, Aug 15 2006