OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..100
FORMULA
a(n) = Sum_{k=0..n} C(2^k,n-k).
Lim_{n->infinity} a(n)^(1/n^2) = 2^(1/4). - Vaclav Kotesovec, Oct 05 2020
G.f.: Sum_{n>=0} ( log(1 + x)^n / n! ) / (1 - 2^n*x). - Paul D. Hanna, Jan 23 2021
MAPLE
A121688:= n-> add(binomial(2^k, n-k), k=0..n); seq(A121688(n), n=0..20); # G. C. Greubel, Mar 15 2021
MATHEMATICA
Table[Sum[Binomial[2^k, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 05 2020 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(2^k, n-k))
(Sage) [sum(binomial(2^k, n-k) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Mar 15 2021
(Magma) [(&+[Binomial(2^k, n-k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Mar 15 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 15 2006
STATUS
approved