A139824 - OEIS

%I #2 Mar 30 2012 18:37:10

%S 1,7,7,7,2,0,8,0,1,6,1,1,9,6,9,1,6,2,6,2,3,1,1,2,5,1,9,7,2,4,4,0,3,5,

%T 3,3,1,2,3,8,0,0,6,4,1,2,5,1,1,2,6,3,1,2,3,3,2,2,9,0,6,6,6,3,2,1,6,2,

%U 0,0,5,5,8,7,8,9,7,5,2,3,4,5,6,7,6,6,4,2,8,5,4,1,7,8,9,6,5,9,4,7,5,0,4,5,1

%N Decimal expansion of constant c = Sum_{n>=0} C(1/2^n, n)*2^n.

%F c = Sum_{n>=0} log(1 + 2/2^n)^n/n! .

%e c = 1.77720801611969162623112519724403533123800641251126312332290666...

%e c = 1 + (1/2)*2 - (3/32)*2^2 + (35/1024)*2^3 - (7285/524288)*2^4 +...

%e c = 1 + log(2) + log(3/2)^2/2! + log(5/4)^3/3! + log(9/8)^4/4! +...

%e The formulas for this constant illustrate the identity:

%e Sum_{n>=0} log(1 + q^n*x)^n*y^n/n! = Sum_{n>=0} binomial(q^n*y, n)*x^n.

%o (PARI) a(n)=local(c=sum(m=0,n+2,log(1+2/2^m)^m/m!));floor(c*10^n)%10

%Y Cf. A139823, A139825.

%K cons,nonn

%O 1,2

%A _Paul D. Hanna_, May 01 2008