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

1,2

Comments

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

Links

Kevin Ryde, Table of n, a(n) for n = 1..500

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.

Example

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

Prog

(PARI) a(n) = (binomial(2*n-1, n-1) + 1) >> (hammingweight(n)==1); \\ Kevin Ryde, Dec 31 2025

Crossrefs

Cf. A001700, A382257 (numerators).

Sequence in context: A121848 A074926 A352932 * A066144 A102343 A023173

Adjacent sequences: A383428 A383429 A383430 * A383432 A383433 A383434

Keyword

nonn,easy,frac

Author

Thomas Ordowski, Apr 27 2025

Status

approved