A353915 Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + arctan(x).

1, -2, -2, -16, -16, 16, -832, -22016, -27648, 173568, -4228608, -57965568, -398991360, 2554896384, -98606039040, -7568860053504, -17762113880064, 200091412463616, -7331825098948608, -258326401420099584, -2009778629489197056, 25949098553870647296, -1278044473427380666368

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Mathematica

nn = 23; f[x_] := Product[1/(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

Crossrefs

Cf. A010050, A353820, A353911, A353913, A353914.

Sequence in context: A361817 A093114 A016740 * A193145 A352348 A133922

Adjacent sequences: A353912 A353913 A353914 * A353916 A353917 A353918

Keyword

sign

Author

Ilya Gutkovskiy, May 10 2022

Status

approved