id:A139825 - OEIS Search Results

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

+0
3

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; cons; graph; listen)

	OFFSET	`1,1`
	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)^23^2/2! + log(9/8)^33^3/3! +...` `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+2, log(1+1/2^m)^m3^m/m!)); floor(c10^n)%10`
	CROSSREFS	`Cf. A139823, A139824.` `Sequence in context: A023844 A132083 A102465 this_sequence A164721 A070072 A095061` `Adjacent sequences: A139822 A139823 A139824 this_sequence A139826 A139827 A139828`
	KEYWORD	`cons,nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2008`

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Last modified November 30 13:13 EST 2009. Contains 167758 sequences.

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