A066384 a(n) = Sum_{k=0..n} binomial(2^n,k).

1, 3, 11, 93, 2517, 242825, 83278001, 100224990433, 423203101008289, 6320756952791172417, 337588530920463407788161, 65183827170777713040896325889, 45946801057461743411385200045344257, 119218150804947710897541255907308439677953, 1146646393160535279886911833912593527834996340737

Offset: 0

Author

N. J. A. Sloane, Dec 23 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n=0..50

Programs

Magma

[(&+[Binomial(2^n, k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Mar 15 2021

Maple

A066384:= n-> add(binomial(2^n, k), k=0..n); seq(A066384(n), n=0..20); # G. C. Greubel, Mar 15 2021

Mathematica

Table[Sum[Binomial[2^n,k], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)

PARI

a(n) = sum(k=0, n, binomial(2^n, k)); \\ Harry J. Smith, Feb 12 2010; modified by G. C. Greubel, Mar 15 2021

Sage

[sum(binomial(2^n, k) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Mar 15 2021

Formula

G.f.: Sum_{n>=0} log(1+2^n*x)^n/((1-2^n*x)*n!). - Paul D. Hanna and Vladeta Jovovic, Jan 15 2008

a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jul 02 2016