A383431 a(n) is the denominator of tanh(Sum_{k=1..n-1} artanh(k/n)), where artanh is the inverse hyperbolic tangent function.

1, 2, 11, 18, 127, 463, 1717, 3218, 24311, 92379, 352717, 1352079, 5200301, 20058301, 77558761, 150270098, 1166803111, 4537567651, 17672631901, 68923264411, 269128937221, 1052049481861, 4116715363801, 16123801841551, 63205303218877, 247959266474053, 973469712824057, 3824345300380221, 15033633249770521

Offset: 1

Author

Thomas Ordowski, Apr 27 2025

Keywords

• nonn
• frac

Comments

a(2^m) is even for m > 0.

Examples

			Denominators of 0, 1/2, 9/11, 17/18, 125/127, 461/463, 1715/1717, 3217/3218, ...
		

Crossrefs

Cf. A001700, A382257 (numerators).

Formula

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.

a(n) = A382257(n) + 1 if n = 2^m or a(n) = A382257(n) + 2 otherwise.