A009399 Expansion of log(1+tanh(x)*x).

0, 2, -20, 576, -33312, 3258880, -485139456, 102300807168, -29028932390912, 10668077137133568, -4929291212351078400, 2797060130323340197888, -1912137417504544127975424, 1550018044651811766917922816

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n) ~ -(-1)^n * sqrt(Pi) * 2^(2*n + 1) * n^(2*n - 1/2) / (r^(2*n) * exp(2*n)), where r = A069855 = 0.8603335890193797624838934241376623334118843632... is the root of the equation r * tan(r) = 1. - Vaclav Kotesovec, Dec 21 2017

Mathematica

With[{nn=30}, Take[CoefficientList[Series[Log[1+Tanh[x]*x], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Jun 13 2016 *)

Crossrefs

Cf. A009379, A069855, A085984.

Sequence in context: A341269 A157317 A350794 * A275779 A292415 A197743

Adjacent sequences: A009396 A009397 A009398 * A009400 A009401 A009402

Keyword

sign

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Prior Mathematica program replaced by Harvey P. Dale, Jun 13 2016

Status

approved