%I #16 Mar 15 2021 21:30:21

%S 1,2,3,6,15,49,210,1191,8981,90405,1219297,22105506,540476679,

%T 17875316557,802011318369,48947781204529,4073596070782653,

%U 463360670014324153,72183972733773232361,15430254274957714069057

%N G.f.: Sum_{n>=0} x^n * (1+x)^(2^n).

%H Vaclav Kotesovec, <a href="/A121688/b121688.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = Sum_{k=0..n} C(2^k,n-k).

%F Lim_{n->infinity} a(n)^(1/n^2) = 2^(1/4). - _Vaclav Kotesovec_, Oct 05 2020

%F G.f.: Sum_{n>=0} ( log(1 + x)^n / n! ) / (1 - 2^n*x). - _Paul D. Hanna_, Jan 23 2021

%p A121688:= n-> add(binomial(2^k,n-k), k=0..n); seq(A121688(n), n=0..20); # _G. C. Greubel_, Mar 15 2021

%t Table[Sum[Binomial[2^k,n-k], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Oct 05 2020 *)

%o (PARI) a(n)=sum(k=0,n,binomial(2^k,n-k))

%o (Sage) [sum(binomial(2^k, n-k) for k in (0..n)) for n in (0..20)] # _G. C. Greubel_, Mar 15 2021

%o (Magma) [(&+[Binomial(2^k, n-k): k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Mar 15 2021

%Y Cf. A136501.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 15 2006