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)).

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

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

Mathematica

x[n_] := x[n] = If[n == 1, 1, (x[n-1] + n)/(1 - n*x[n-1])];
a[n_] := Denominator[x[n]];
Table[a[n], {n, 1, 29}] (* Jean-François Alcover, Aug 09 2023 *)

Crossrefs

For numerators see A180657.

Sequence in context: A157889 A361677 A255897 * A294460 A373720 A118593

Adjacent sequences: A220444 A220445 A220446 * A220448 A220449 A220450

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 22 2012

Status

approved