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A220447 Define sequence x(n) by x(1)=1, thereafter x(n) = (x(n-1)+n)/(1-n*x(n-1)); sequence gives denominator(x(n)). 4
1, 1, 1, 1, 19, 73, 331, 43, 281, 4511, 10873, 322921, 12179, 720817, 538759, 87995911, 1185403, 37171235, 46336951, 6986985769, 2602576465, 243540693677, 181777598557, 13097400661955, 135996437150855, 8249498995171439, 56213506181241631, 601615828819880125, 10365435567354511181 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

x(n) = tan( sum_{k=1..n} arctan(k)): see A180657.

LINKS

Table of n, a(n) for n=1..29.

V. H. Moll, An arithmetic conjecture on a sequence of arctangent sums, 2012.

EXAMPLE

The x(n) sequence begins 1, -3, 0, 4, -9/19, 105/73, -308/331, 36/43, -423/281, 2387/4511, -26004/10873,  ...

MAPLE

x:=proc(n) option remember;

if n=1 then 1 else (x(n-1)+n)/(1-n*x(n-1)); fi; end;

s1:=[seq(x(n), n=1..30)]; # x(n)

s2:=map(numer, s1); # A180657

s3:=map(denom, s1); # A220447

CROSSREFS

For numerators see A180657.

Sequence in context: A178541 A157889 A255897 * A294460 A118593 A047979

Adjacent sequences:  A220444 A220445 A220446 * A220448 A220449 A220450

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Dec 22 2012

STATUS

approved

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Last modified July 22 10:03 EDT 2019. Contains 325219 sequences. (Running on oeis4.)