A012269 Expansion of e.g.f.: arctan(log(x+1)*log(x+1)).

0, 0, 2, -6, 22, -100, 308, 1512, -51144, 869472, -12406608, 155319120, -1563312720, 6008315040, 296596492320, -12739805608320, 357984190838400, -8317532611046400, 160961311569285120, -2183410259228574720

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..425

Formula

a(n) ~ (n-1)! * (-1)^(n+1) * sin(n*arctan(sin(1/sqrt(2)) / (cos(1/sqrt(2)) - exp(1/sqrt(2))))) * (exp(1/sqrt(2)) / sqrt(1 + exp(sqrt(2)) - 2*exp(1/sqrt(2)) * cos(1/sqrt(2))))^n. - Vaclav Kotesovec, Jan 02 2014

Example

arctan(log(x+1)*log(x+1)) = 2/2!*x^2-6/3!*x^3+22/4!*x^4-100/5!*x^5...

Maple

seq(coeff(series(factorial(n)*arctan(log(x+1)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 28 2018

Mathematica

With[{nn=20}, CoefficientList[Series[ArcTan[Log[x+1]^2], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Feb 24 2013 *)

Prog

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(atan(log(x+1)^2)))) \\ G. C. Greubel, Oct 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arctan(Log(x+1)^2) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 28 2018

Crossrefs

Sequence in context: A189844 A189282 A318974 * A012272 A009789 A012271

Adjacent sequences: A012266 A012267 A012268 * A012270 A012271 A012272

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Extensions

Corrected and definition clarified by Harvey P. Dale, Feb 24 2013

Status

approved