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A292817 b(0) = 1, b(2*n-1) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2/(...+(n-1)^2/(1+n^2)))))) and b(2*n) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2/(...+n^2/(1+n^2)))))). a(n) is the denominator of b(n). 1
1, 2, 3, 11, 23, 61, 329, 2281, 2515, 32285, 253195, 2577715, 11692735, 69000385, 78993865, 9542994065, 55043460305, 414012989785, 1057309252855, 17617828844255, 5873750196655, 1127553022142305, 17180305293984965, 341915575670968805 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The limit of b(n) is (PolyGamma(1,(1+sqrt(5))/4)-PolyGamma(1,(3+sqrt(5))/4))/2. See A091659.

LINKS

Table of n, a(n) for n=0..23.

Eric Weisstein's World of Mathematics, Polygamma Function

Eric Weisstein's World of Mathematics, Ramanujan Continued Fractions

EXAMPLE

b(0) = 1/1, so a(0) = 1.

b(1) = 1/(1+1^2) = 1/2, so a(1) = 2.

b(2) = 1/(1+1^2/(1+1^2)) = 2/3, so a(2) = 3.

b(3) = 1/(1+1^2/(1+1^2/(1+2^2))) = 6/11, so a(3) = 11.

b(4) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2)))) = 14/23, so a(4) = 23.

CROSSREFS

Cf. A091659, A292816.

Sequence in context: A119641 A252005 A074496 * A292112 A065849 A136402

Adjacent sequences:  A292814 A292815 A292816 * A292818 A292819 A292820

KEYWORD

nonn,frac

AUTHOR

Seiichi Manyama, Sep 24 2017

STATUS

approved

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Last modified February 23 02:29 EST 2019. Contains 320411 sequences. (Running on oeis4.)