A013563 Expansion of e.g.f. arctan(log(x+1)/exp(x)).

1, -3, 6, 12, -317, 2915, -11886, -171920, 5115653, -68721223, 210613062, 17051988316, -550238104665, 8495695565695, 24062949136594, -6101110377673856, 206210494097275657, -3111467353854907467

Offset

1,2

Comments

The inner function is log(x+1)/exp(x) = 2*x/1! - 9*x^2/2! + 32*x^3/3! - 120*x^4/4! + 534*x^5/5! - 2905*x^6/6! + 18976*x^7/7! ...

Links

G. C. Greubel, Table of n, a(n) for n = 1..200

Formula

E.g.f.: arctan(log(x+1)/exp(x)).

Example

x - 3/2!*x^2 + 6/3!*x^3 + 12/4!*x^4 - 317/5!*x^5 + ...

Mathematica

CoefficientList[Series[ArcTan[Log[x + 1]/Exp[x]], {x, 0, 20}], x]*Range[0, 20]! (* G. C. Greubel, Nov 13 2016 *)

Crossrefs

Sequence in context: A282231 A301522 A139416 * A009788 A102966 A309719

Adjacent sequences: A013560 A013561 A013562 * A013564 A013565 A013566

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com), Dec 11 1996

Status

approved