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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
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
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
Sequence in context: A119641 A252005 A074496 * A292112 A363141 A374914
KEYWORD
nonn,frac
AUTHOR
Seiichi Manyama, Sep 24 2017
STATUS
approved