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

Author

Paul D. Hanna, May 01 2008

Keywords

• cons
• nonn

Examples

			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.
		

Crossrefs

Cf. A139823, A139824.

Programs

PARI

a(n)=local(c=sum(m=0,n+2,log(1+1/2^m)^m*3^m/m!));floor(c*10^n)%10

Formula

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