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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
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
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
Sequence in context: A177790 A307068 A269506 * A105635 A178320 A297187
KEYWORD
nonn,frac
AUTHOR
Seiichi Manyama, Sep 24 2017
STATUS
approved