A353819 Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + arcsinh(x).

1, 0, -1, 4, -11, 66, -547, 4880, -27351, 263310, -3258663, 39791016, -390445563, 5477278548, -84140635815, 1486404086016, -18431412645519, 322018685539542, -6436900596281679, 133183534639917240, -2208721087854287811, 49383164607876494604, -1149793471388581053219

Offset: 1

Author

Ilya Gutkovskiy, May 08 2022

Keywords

• sign

Crossrefs

Cf. A001818, A006973, A137852, A353608, A353818, A353820, A353821.

Programs

Mathematica

nn = 23; f[x_] := Product[(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