A293192 a(n) = n! * [x^n] exp(n*arctan(x)).

1, 1, 4, 21, 128, 745, 1440, -89075, -3031040, -76951215, -1784742400, -39056351675, -785147904000, -12815410658375, -64977212518400, 8229576066616125, 587339977981952000, 29185361934747006625, 1256364637107240960000, 48860370609512175371125, 1686271331087959982080000

Offset: 0

Author

Ilya Gutkovskiy, Oct 02 2017

Keywords

• sign

Crossrefs

Cf. A002019.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[n ArcTan[x]], {x, 0, n}], {n, 0, 20}]
Table[n! SeriesCoefficient[Exp[n Sum[(-1)^k x^(2 k + 1)/(2 k + 1), {k, 0, Infinity}]], {x, 0, n}], {n, 0, 20}]