A139825 Decimal expansion of constant c = Sum_{n>=0} C(3/2^n, n).

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

Offset

1,1

Links

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

Formula

c = Sum_{n>=0} log(1 + 1/2^n)^n*3^n/n! .

Example

c = 2.44786260575157703503227005649125153516326296494143146338838167...
c = 1 + 3/2 - 3/32 + 65/1024 - 16965/524288 + 4112925/268435456 +...
c = 1 + log(3/2)*3 + log(5/4)^2*3^2/2! + log(9/8)^3*3^3/3! +...
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+1/2^m)^m*3^m/m!)); floor(c*10^n)%10

Crossrefs

Cf. A139823, A139824.

Sequence in context: A132083 A286014 A102465 * A347067 A164721 A194118

Adjacent sequences: A139822 A139823 A139824 * A139826 A139827 A139828

Keyword

cons,nonn

Author

Paul D. Hanna, May 01 2008

Status

approved