A296438 Expansion of e.g.f. log(1 + arctan(x))*exp(x).

0, 1, 1, 0, 0, 13, 5, -336, -56, 18593, -6735, -1598520, 1192664, 205475645, -255011835, -36324220856, 62049925040, 8519764352097, -18835422533375, -2551646722754512, 6927586371061712, 951619735931190157, -3077560879933239899, -432185107142832520576, 1624964470900980885432

Offset: 0

Author

Ilya Gutkovskiy, Dec 12 2017

Keywords

• sign

Examples

			E.g.f.: A(x) = x/1! + x^2/2! + 13*x^5/5! + 5*x^6/6! - 336*x^7/7! - 56*x^8/8! + ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A009371, A009374, A009390, A110708, A279927, A296439.

Programs

Maple

a:=series(log(1+arctan(x))*exp(x),x=0,25): seq(n!*coeff(a,x,n),n=0..24); # Paolo P. Lava, Mar 27 2019

Mathematica

nmax = 24; CoefficientList[Series[Log[1 + ArcTan[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[Log[1 + I (Log[1 - I x] - Log[1 + I x])/2] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!

PARI

my(ox=O(x^30)); Vecrev(Pol(serlaplace(log(1 + atan(x + ox)) * exp(x + ox)))) \\ Andrew Howroyd, Dec 12 2017

Formula

E.g.f.: log(1 + i*(log(1 - i*x) - log(1 + i*x))/2)*exp(x), where i is the imaginary unit.