A013235 E.g.f. arcsin(log(x+1)-tan(x))=-1/2!*x^2-6/4!*x^4+8/5!*x^5-135/6!*x^6...

0, 0, -1, 0, -6, 8, -135, 448, -6300, 35408, -503685, 4051168, -61966674, 652583384, -10926862947, 142548422560, -2622105365880, 40794310136480, -822873495765321, 14853219468665920, -327327482638812190

Offset

0,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200 (corrected by Sean A. Irvine, Jan 18 2019)

Formula

a(n) ~ n! * (-1)^(n+1) * c / (n^(3/2) * r^n), where r = 0.8940624905708084527840316322153248827767719... is the root of the equation log(1-r) + tan(r) = -1, c = 0.990137045203584985078038586884002826628... . - Vaclav Kotesovec, Feb 04 2015

Mathematica

With[{nn=20}, Drop[CoefficientList[Series[ArcSin[Log[x+1]-Tan[x]], {x, 0, nn}], x]Range[0, nn]!, 2]] (* Harvey P. Dale, Jan 29 2012 *)

Prog

(PARI) x='x+O('x^33); concat([0, 0], Vec(serlaplace(asin(log(x+1)-tan(x))))) /* Joerg Arndt, Jan 30 2012 */

Crossrefs

Sequence in context: A324987 A382959 A013239 * A257869 A201387 A013236

Adjacent sequences: A013232 A013233 A013234 * A013236 A013237 A013238

Keyword

sign

Author

Patrick Demichel

Extensions

a(0)=a(1)=0 inserted by Sean A. Irvine, Aug 01 2018

Status

approved