A354066 - OEIS

%I #6 May 17 2022 07:25:55

%S 1,-2,-2,8,-24,224,-720,-1408,0,717824,-3628800,-47546368,-479001600,

%T 12431673344,87178291200,-68669145088,-20922789888000,47215125069824,

%U -6402373705728000,-159504062197792768,2432902008176640000,102176932845365755904,-1124000727777607680000

%N Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + tanh(x).

%F E.g.f.: Sum_{k>=1} mu(k) * log(1 + tanh(x^k)) / k.

%t nmax = 23; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + Tanh[x^k]]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

%Y Cf. A000182, A353779, A353912, A354055, A354056, A354063, A354064, A354065.

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, May 16 2022