A353928 Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + arctanh(x).

1, -2, 2, -32, 64, -464, 3968, -92672, 414720, -5486592, 68247552, -869895168, 15949529088, -299609505792, 5012834549760, -177156842717184, 2119956936523776, -50954009373573120, 1123874181449515008, -29311973327486582784, 730049769522063212544, -22005690087484302557184

Offset: 1

Author

Ilya Gutkovskiy, May 11 2022

Keywords

• sign

Crossrefs

Cf. A010050, A353821, A353912, A353913, A353914, A353915.

Programs

Mathematica

nn = 22; f[x_] := Product[1/(1 - a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - ArcTanh[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten