A012312 Expansion of e.g.f. arctanh(arcsin(x) * log(x+1)).

0, 0, 2, -3, 12, -40, 478, -3759, 40152, -387864, 5203962, -70961715, 1142838180, -18621542160, 342700299030, -6622936396335, 140637395893680, -3129194141386320, 74723900156463090, -1873298738386231875

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..426

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)*arctanh(arcsin(x)*log(x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 25 2018

Mathematica

With[{nn = 30}, CoefficientList[Series[ArcTanh[ArcSin[x] Log[x + 1]], {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, Oct 25 2018 *)

Prog

(PARI) x='x+O('x^30); concat([0, 0], Vec(serlaplace(atanh(asin(x)* log(x+1)) ))) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Argtanh(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: A012512 A012516 A012306 * A009243 A232864 A371612

Adjacent sequences: A012309 A012310 A012311 * A012313 A012314 A012315

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