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A269481 Continued fraction expansion of the Dirichlet eta function at 4. 0
0, 1, 17, 1, 7, 3, 3, 1, 7, 3, 6, 1, 1, 7, 1, 11, 1, 11, 5, 1, 2, 2, 2, 7, 1, 14, 6, 5, 1, 1, 1, 1, 10, 9, 1, 1, 5, 2, 2, 3, 2, 5, 2, 4, 1, 46, 312, 3, 3, 1, 15, 1, 2, 5, 2, 1, 1, 27, 1, 2, 1, 2, 11, 5, 2, 1, 482, 3, 2, 4, 2, 2, 3, 1, 3, 1, 2, 1, 1, 13, 1, 13, 1, 1, 67, 149, 7, 2, 2, 18, 1, 2, 1, 1, 1, 51, 1, 7, 1, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Continued fraction of Sum_{k>=1} (-1)^(k - 1)/k^4 = (7*Pi^4)/720 = 0.9470328294972459175765...

LINKS

Table of n, a(n) for n=0..99.

OEIS Wiki, Euler's alternating zeta function

Eric Weisstein's World of Mathematics, Dirichlet Eta Function

Wikipedia, Dirichlet Eta Function

Index entries for continued fractions for constants

EXAMPLE

1/1^4 - 1/2^4 + 1/3^4 - 1/4^4 + 1/5^4 - 1/6^4 +... = 1/(1 + 1/(17 + 1/(1 + 1/(7 + 1/(3 + 1/(3 + 1/...)))))).

MATHEMATICA

ContinuedFraction[(7 Pi^4)/720, 100]

CROSSREFS

Cf. A013680, A267315.

Sequence in context: A040301 A175960 A040302 * A229201 A040303 A040304

Adjacent sequences:  A269478 A269479 A269480 * A269482 A269483 A269484

KEYWORD

nonn,cofr

AUTHOR

Ilya Gutkovskiy, Feb 27 2016

STATUS

approved

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Last modified September 17 16:57 EDT 2019. Contains 327136 sequences. (Running on oeis4.)