A353821 Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + arctanh(x).

1, 0, 2, -8, 64, -384, 3968, -34432, 414720, -4454400, 68247552, -912236544, 15949529088, -245572583424, 5012834549760, -92436465352704, 2119956936523776, -42836227522560000, 1123874181449515008, -26161653829651660800, 730049769522063212544, -18719979459270521389056

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Mathematica

nn = 22; f[x_] := Product[(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

Crossrefs

Cf. A006973, A010050, A137852, A353779, A353818, A353819, A353820.

Sequence in context: A287229 A323853 A354276 * A354237 A191570 A052707

Adjacent sequences: A353818 A353819 A353820 * A353822 A353823 A353824

Keyword

sign

Author

Ilya Gutkovskiy, May 08 2022

Status

approved