A353914 Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + arcsinh(x).

1, -2, -1, -20, -11, 46, -547, -29840, -27351, 232818, -3258663, -29911848, -390445563, 4450393260, -84140635815, -12153983817984, -18431412645519, 286688710444842, -6436900596281679, -169286474970429624, -2208721087854287811, 41892263643715799796, -1149793471388581053219

Offset: 1

Author

Ilya Gutkovskiy, May 10 2022

Keywords

• sign

Crossrefs

Cf. A001818, A353819, A353910, A353913, A353915.

Programs

Mathematica

nn = 23; f[x_] := Product[1/(1 - a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - ArcSinh[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten