id:A139823 - OEIS Search Results

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

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1, 4, 3, 0, 6, 3, 4, 5, 2, 4, 3, 6, 1, 1, 6, 8, 6, 5, 7, 0, 6, 6, 1, 8, 0, 3, 3, 7, 5, 5, 9, 0, 2, 9, 5, 5, 4, 7, 0, 6, 8, 7, 3, 0, 9, 8, 5, 0, 5, 3, 9, 8, 7, 9, 1, 7, 6, 0, 7, 5, 5, 4, 5, 8, 9, 2, 6, 8, 9, 4, 6, 7, 1, 8, 1, 4, 9, 9, 5, 5, 8, 2, 1, 5, 4, 3, 6, 5, 4, 4, 9, 2, 6, 2, 1, 8, 6, 6, 8, 1, 3, 4, 3, 7, 1 (list; cons; graph; listen)

	OFFSET	`1,2`
	FORMULA	`c = Sum_{n>=0} log(1 + 1/2^n)^n/n! .`
	EXAMPLE	`c = 1.43063452436116865706618033755902955470687309850539879176075545...` `c = 1 + 1/2 - 3/32 + 35/1024 - 7285/524288 + 1570863/268435456 -+...` `c = 1 + log(3/2) + log(5/4)^2/2! + log(9/8)^3/3! + log(17/16)^4/4! +...` `The formulas for this constant illustrate the identity:` `Sum_{n>=0} log(1 + q^nx)^ny^n/n! = Sum_{n>=0} binomial(q^ny, n)x^n.`
	PROGRAM	`(PARI) a(n)=local(c=sum(m=0, n, log(1+1/2^m)^m/m!)); floor(c*10^n)%10`
	CROSSREFS	`Cf. A139824, A139825.` `Adjacent sequences: A139820 A139821 A139822 this_sequence A139824 A139825 A139826` `Sequence in context: A016697 A086466 A021703 this_sequence A019756 A010650 A011091`
	KEYWORD	`cons,nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2008`

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Last modified October 7 14:39 EDT 2008. Contains 144666 sequences.

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