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

Author

N. J. A. Sloane, Dec 22 2012

Keywords

• nonn
• frac

Comments

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

Examples

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

Links

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

Crossrefs

For numerators see A180657.

Programs

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 *)