A348140 a(n) is the numerator of tan(n * arctan(1/n)).

1, 4, 13, 240, 719, 42372, 92567, 14970816, 21475201, 8825080100, 7836127861, 7809130867824, 4132643140079, 9678967816041188, 2973238691433583, 16000787866533953280, 2798084251807349761, 34017524842099233036996, 3336132453587291393821, 90417110945911655996319600

Offset: 1

Author

Amiram Eldar, Oct 02 2021

Keywords

• nonn
• frac

Examples

			The fractions begin with 1, 4/3, 13/9, 240/161, 719/475, 42372/27755, 92567/60319, 14970816/9722113, 21475201/13913289, 8825080100/5707904499, ...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..387

Crossrefs

Cf. A049471, A348131, A348132, A348141 (denominators).

Programs

Mathematica

f[n_] := Module[{s = 1/n}, Do[s = (s + 1/n)/(1 - s/n), {k, 1, n - 1}]; s]; Numerator @ Array[f, 20]

Formula

Lim_{n->oo} a(n)/A348141(n) = tan(1) (A049471).