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%I #26 Oct 03 2022 07:43:44
%S -1,6,210,12012,831402,63740820,5209363380,444799488600,
%T 39209074920090,3541117629057540,325969196485349340,
%U 30471769822097981160,2884881686418189303300,276043232874562618320072
%N Expansion of -1/x + 6*3F2( 5/6, 1, 7/6; 3/2, 2; 108*x).
%H G. C. Greubel, <a href="/A028350/b028350.txt">Table of n, a(n) for n = -1..250</a>
%F 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
%F 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
%p 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;
%t 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 *)
%t 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_ *)
%K sign
%O -1,2
%A _N. J. A. Sloane_
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