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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
OFFSET
1,5
COMMENTS
x(n) = tan( sum_{k=1..n} arctan(k)): see A180657.
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
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Dec 22 2012
STATUS
approved