A012307 Expansion of e.g.f. arctan(arcsin(x) * log(x+1)).

0, 0, 2, -3, 12, -40, -2, 1281, -20328, 247176, -2335878, 18296685, -30050460, -2786088240, 84018996150, -1739881819935, 29231087119920, -366680093070480, 1450522417769970, 113001315573589245

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..435

Example

E.g.f. = 2*x^2/2! - 3*x^3/3! + 12*x^4/4! - 40*x^5/5! + ...

Maple

seq(coeff(series(factorial(n)*arctan(arcsin(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 25 2018

Mathematica

With[{nn=20}, CoefficientList[Series[ArcTan[ArcSin[x]Log[x+1]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 21 2018 *)

Prog

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(atan(asin(x)* log(x+1))))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Arctan(Arcsin(x)*Log(x+1)) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Oct 25 2018

Crossrefs

Sequence in context: A099171 A268561 A352099 * A012311 A012513 A012515

Adjacent sequences: A012304 A012305 A012306 * A012308 A012309 A012310

Keyword

sign

Author

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

Extensions

a(0) and a(1) inserted and title improved by Sean A. Irvine, Jul 17 2018

Status

approved