OFFSET
1,4
FORMULA
a(3*n+1) = (3*n)!, a(3*n+2) = -(3*n+1)!, a(3*n) = 0.
E.g.f.: A(x) = 2*sqrt(3)/3*arctan(sqrt(3)*x/(x+2)) = x-x^2/2!+6*x^4/4!-24*x^5/5!+720*x^7/7!-....
The derivative A'(x) = 1/(1+x+x^2). The inverse function A^-1(x) = 2/sqrt(3)*tan(sqrt(3)/2*x)/(1-1/sqrt(3)*tan(sqrt(3)/2*x)) is the generating function for A080635 (apart from the initial term).
D-finite with recurrence: a(n) +(n-1)*a(n-1) +(n-1)*(n-2)*a(n-2)=0. - R. J. Mathar, Jan 25 2020
MATHEMATICA
With[{nn=30}, Rest[CoefficientList[Series[2 Sqrt[3]/3 ArcTan[Sqrt[ 3] x/(x+2)], {x, 0, nn}], x] Range[0, nn-1]!]] (* Harvey P. Dale, May 13 2019 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Peter Bala, Sep 02 2011
STATUS
approved