A013073 Expansion of e.g.f. arctan(arcsinh(x) + log(x+1)).

0, 2, -1, -15, 42, 661, -4890, -66619, 1034936, 11317021, -345817440, -2547339861, 165729594888, 460712169615, -106781858632176, 333854778870681, 88033258608789600, -955215842270538663

Offset

0,2

Links

Muniru A Asiru, Table of n, a(n) for n = 0..100

Example

2*x - 1/2!*x^2 - 15/3!*x^3 + 42/4!*x^4 + 661/5!*x^5 ...

Maple

seq(coeff(series(factorial(n)*arctan(arcsinh(x)+log(x+1)), x, n+1), x, n), n=0..20); # Muniru A Asiru, Jul 30 2018

Mathematica

With[{nn=30}, CoefficientList[Series[ArcTan[ArcSinh[x]+Log[x+1]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 12 2021 *)

Prog

(PARI) x = 'x + O('x^30); concat([0], Vec(serlaplace(atan(asinh(x) + log(x+1))))) \\ Michel Marcus, Jul 30 2018

Crossrefs

Sequence in context: A012894 A013076 A012890 * A184232 A074952 A078074

Adjacent sequences: A013070 A013071 A013072 * A013074 A013075 A013076

Keyword

sign

Author

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

Extensions

a(0)=0 inserted and title improved by Sean A. Irvine, Jul 30 2018

Status

approved