A013430 Expansion of e.g.f. exp(arcsin(x)-arctanh(x)).

1, 0, 0, -1, 0, -15, 10, -495, 840, -29575, 87750, -2805075, 12340900, -387547875, 2304422250, -73485787375, 556725078000, -18311017515375, 169707184396750, -5801182757296875, 63859173696337500

Offset: 0

Author

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

Keywords

• sign

Examples

			1-1/3!*x^3-15/5!*x^5+10/6!*x^6-495/7!*x^7...
		

Crossrefs

Cf. A006228, A013170.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[ArcSin[x]-ArcTanh[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 23 2025 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(asin(x)-atanh(x)))) \\ Michel Marcus, May 10 2020

Formula

a(n) = (-1)^n * (A006228(n+1) - n * A006228(n)). - Mark van Hoeij, Aug 27 2005