This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383431 #12 Apr 29 2025 12:52:10
%S A383431 1,2,11,18,127,463,1717,3218,24311,92379,352717,1352079,5200301,
%T A383431 20058301,77558761,150270098,1166803111,4537567651,17672631901,
%U A383431 68923264411,269128937221,1052049481861,4116715363801,16123801841551,63205303218877,247959266474053,973469712824057,3824345300380221,15033633249770521
%N A383431 a(n) is the denominator of tanh(Sum_{k=1..n-1} artanh(k/n)), where artanh is the inverse hyperbolic tangent function.
%C A383431 a(2^m) is even for m > 0.
%F A383431 a(n) = (binomial(2n-1, n-1) + 1)/2 if n = 2^m or a(n) = binomial(2n-1, n-1) + 1 otherwise, because tanh(Sum_{k=1..n-1} artanh(k/n)) = (binomial(2n-1, n-1) - 1)/(binomial(2n-1, n-1) + 1) reduced.
%F A383431 a(n) = A382257(n) + 1 if n = 2^m or a(n) = A382257(n) + 2 otherwise.
%e A383431 Denominators of 0, 1/2, 9/11, 17/18, 125/127, 461/463, 1715/1717, 3217/3218, ...
%Y A383431 Cf. A001700, A382257 (numerators).
%K A383431 nonn,frac
%O A383431 1,2
%A A383431 _Thomas Ordowski_, Apr 27 2025