A013170 Expansion of e.g.f.: exp(arctanh(x)+arcsin(x)).

1, 2, 4, 11, 40, 185, 1030, 6785, 51160, 438425, 4176250, 44098925, 507867100, 6375156125, 86130937750, 1253044612625, 19429666282000, 321457635604625, 5626346310003250, 104323833636303125, 2034312191276462500

Offset: 0

Author

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

Keywords

• nonn

Examples

			exp(arctanh(x)+arcsin(x)) = 1+2*x+4/2!*x^2+11/3!*x^3+40/4!*x^4+185/5!*x^5+...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A006228.

Programs

Mathematica

Table[n!*SeriesCoefficient[E^(ArcTanh[x]+ArcSin[x]),{x,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 07 2012 *)

PARI

x='x+O('x^66); Vec(serlaplace(exp(atanh(x)+asin(x)))) \\ Joerg Arndt, May 04 2013

Formula

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

a(n) = (n^2-3*n+5)*a(n-2) + (n^2-6*n+10)*a(n-3). - Vaclav Kotesovec, Oct 07 2012