OFFSET
-1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..250
FORMULA
D-finite with recurrence (n+1)*(2*n+1)*a(n) -6*(6*n-1)*(6*n+1)*a(n-1)=0. - R. J. Mathar, Jul 27 2022
G.f.: -sqrt(3)/(2*x)*((2*sqrt(-x)+sqrt(1-108*x)/3^(3/2))^(1/3)+1/(3*(2*sqrt(-x)+sqrt(1-108*x)/3^(3/2))^(1/3))). - Vladimir Kruchinin, Oct 03 2022
MAPLE
a := proc(n) option remember; if n = -1 then -1 else 6*(6*n - 1)*(6*n + 1)*a(n - 1)/((n + 1)*(2*n + 1)) fi; end;
MATHEMATICA
nxt[{n_, a_}]:={n+1, (6*a*(5+6*n)*(7+6*n))/((2+n)*(3+2*n))}; Join[ {-1}, Transpose[NestList[nxt, {0, 6}, 15]][[2]]] (* Harvey P. Dale, May 10 2013 *)
Table[SeriesCoefficient[-(Sqrt[3]*(1/(3*(Sqrt[1 - 108*x]/(3*Sqrt[3]) + 2*Sqrt[-x])^(1/3)) + (Sqrt[1 - 108*x]/(3*Sqrt[3]) + 2*Sqrt[-x])^(1/3)))/(2*x), {x, 0, n}], {n, -1, 15}] (* Vaclav Kotesovec, Oct 03 2022, after Vladimir Kruchinin *)
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved