OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..59
FORMULA
G.f.: Sum_{n>=0} log(1+(2^n+1)*x)^n/n!.
From Vaclav Kotesovec, Jul 02 2016: (Start)
a(n) ~ binomial(2^n,n).
a(n) ~ 2^(n^2) / n!.
a(n) ~ 2^(n^2 - 1/2) * exp(n) / (sqrt(Pi) * n^(n+1/2)).
(End)
MAPLE
a:=proc(n) options operator, arrow: sum(binomial(n, k)*binomial(2^k, n), k=0..n) end proc: seq(a(n), n=0..13); # Emeric Deutsch, Jan 27 2008
MATHEMATICA
Table[Sum[Binomial[n, k]*Binomial[2^k, n], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)
PROG
(PARI) for(n=0, 25, print1(sum(k=0, n, binomial(n, k)*binomial(2^k, n)), ", ")) \\ G. C. Greubel, Mar 21 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul D. Hanna and Vladeta Jovovic, Jan 13 2008
EXTENSIONS
More terms from Emeric Deutsch, Jan 27 2008
STATUS
approved