A174785 Expansion of g.f. (1+2*x-x^2+x^3-x^4-x^5)/(1+x^3)^2.

1, 2, -1, -1, -5, 1, 1, 8, -1, -1, -11, 1, 1, 14, -1, -1, -17, 1, 1, 20, -1, -1, -23, 1, 1, 26, -1, -1, -29, 1, 1, 32, -1, -1, -35, 1, 1, 38, -1, -1, -41, 1, 1, 44, -1, -1, -47, 1, 1, 50, -1, -1, -53, 1, 1, 56, -1, -1, -59, 1, 1, 62, -1, -1, -65, 1, 1, 68, -1, -1

Offset: 0

Author

Paul Barry, Mar 29 2010

Keywords

• easy
• sign

Comments

Hankel transform of A174783.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,-2,0,0,-1).

Crossrefs

Cf. A174783.

Programs

Mathematica

CoefficientList[Series[(1+2x-x^2+x^3-x^4-x^5)/(1+x^3)^2,{x,0,50}],x] (* or *) LinearRecurrence[{0,0,-2,0,0,-1},{1,2,-1,-1,-5,1},60] (* Harvey P. Dale, May 11 2019 *)

Formula

a(n) = (n+4)*cos(pi*n/3)/3 + n*sin(pi*n/3)/sqrt(3) - (n+1)*(-1)^n/3.

E.g.f.: exp(-x)*(2*exp(3*x/2)*(2 + x)*cos(sqrt(3)*x/2) + x - 1)/3. - Stefano Spezia, May 29 2024

Extensions

a(51)-a(69) from Stefano Spezia, May 29 2024