A353912 Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + tanh(x).

1, -2, -2, -16, -24, 64, -720, -23808, -35840, 282368, -3628800, -75458560, -479001600, 5315078144, -82614884352, -8601835798528, -20922789888000, 321288633450496, -6402373705728000, -309168395474436096, -2379913632645120000, 46441359567137275904

Offset: 1

Author

Ilya Gutkovskiy, May 10 2022

Keywords

• sign

Crossrefs

Cf. A155585, A353779, A353873, A353910, A353911.

Programs

Mathematica

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