A353820 Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + arctan(x).

1, 0, -2, 8, -16, 96, -832, 9344, -27648, 238080, -4228608, 55812096, -398991360, 4930609152, -98606039040, 2440552022016, -17762113880064, 235149341884416, -7331825098948608, 170578782435409920, -2009778629489197056, 38563016760590598144, -1278044473427380666368

Offset: 1

Author

Ilya Gutkovskiy, May 08 2022

Keywords

• sign

Crossrefs

Cf. A006973, A010050, A137852, A353611, A353818, A353819, A353821.

Programs

Mathematica

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