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A292816 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 numerator of b(n). 1
1, 1, 2, 6, 14, 34, 194, 1282, 1462, 18218, 146086, 1457782, 6716878, 39074098, 45252802, 5408759762, 31474373714, 234791957218, 603801637054, 9995479925774, 3351221125294, 639914357324914, 9795281594021882, 194090616503597114, 1604611166042748122 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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..24.

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) = 1.

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

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

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

CROSSREFS

Cf. A091659, A292817.

Sequence in context: A186523 A177790 A269506 * A105635 A178320 A297187

Adjacent sequences:  A292813 A292814 A292815 * A292817 A292818 A292819

KEYWORD

nonn,frac

AUTHOR

Seiichi Manyama, Sep 24 2017

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)