A139824 Decimal expansion of constant c = Sum_{n>=0} C(1/2^n, n)*2^n.

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, 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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

Formula

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

Example

c = 1.77720801611969162623112519724403533123800641251126312332290666...
c = 1 + (1/2)*2 - (3/32)*2^2 + (35/1024)*2^3 - (7285/524288)*2^4 +...
c = 1 + log(2) + log(3/2)^2/2! + log(5/4)^3/3! + log(9/8)^4/4! +...
The formulas for this constant illustrate the identity:
Sum_{n>=0} log(1 + q^n*x)^n*y^n/n! = Sum_{n>=0} binomial(q^n*y, n)*x^n.

Prog

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

Crossrefs

Cf. A139823, A139825.

Sequence in context: A019860 A011422 A051726 * A019799 A341908 A216159

Adjacent sequences: A139821 A139822 A139823 * A139825 A139826 A139827

Keyword

cons,nonn

Author

Paul D. Hanna, May 01 2008

Status

approved