A121688 G.f.: Sum_{n>=0} x^n * (1+x)^(2^n).

1, 2, 3, 6, 15, 49, 210, 1191, 8981, 90405, 1219297, 22105506, 540476679, 17875316557, 802011318369, 48947781204529, 4073596070782653, 463360670014324153, 72183972733773232361, 15430254274957714069057

Offset: 0

Author

Paul D. Hanna, Aug 15 2006

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A136501.

Programs

Magma

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

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

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