A012287 Expansion of e.g.f. arctanh(sin(x)*log(x+1))=2/2!*x^2-3/3!*x^3+4/4!*x^4-20/5!*x^5...

0, 0, 2, -3, 4, -20, 350, -3171, 21320, -172080, 2459578, -38861515, 540169100, -7467693012, 125140866006, -2480288923035, 50275271244432, -1015574149625984, 21888753352226418, -522647511904669491

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..430

Formula

a(n) ~ (n-1)! * (-1)^n / (2 * r^n), where r = 0.7642695126688585683463... is the root of the equation log(1-r)*sin(r) = -1. - Vaclav Kotesovec, Feb 05 2015

Example

E.g.f. = 2*x^2/2! - 3*x^3/3! + 4*x^4/4! - 20*x^5/5! + ...

Mathematica

CoefficientList[Series[ArcTanh[Log[1 + x]*Sin[x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 05 2015 *)

Prog

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(atanh(sin(x)* log(x+1))))) \\ G. C. Greubel, Oct 26 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argtanh(Sin(x)*Log(x+1)) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 26 2018

Crossrefs

Sequence in context: A244673 A012574 A012282 * A012575 A012580 A246391

Adjacent sequences: A012284 A012285 A012286 * A012288 A012289 A012290

Keyword

sign

Author

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

Extensions

Prepended missing a(0)=a(1)=0 from Vaclav Kotesovec, Feb 05 2015

Status

approved