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A139825
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Decimal expansion of constant c = Sum_{n>=0} C(3/2^n, n).
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2
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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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| c = Sum_{n>=0} log(1 + 1/2^n)^n*3^n/n! .
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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.
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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
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CROSSREFS
| Cf. A139823, A139824.
Sequence in context: A023844 A132083 A102465 * A164721 A194118 A070072
Adjacent sequences: A139822 A139823 A139824 * A139826 A139827 A139828
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KEYWORD
| cons,nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2008
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