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A095776 Expansion of (1-9x-27x^3)^(-1/3). 0

%I #24 Sep 08 2022 08:45:13

%S 1,3,18,135,1053,8505,70470,594135,5073840,43761870,380433024,

%T 3328474032,29276671347,258669163665,2294194659012,20415148177023,

%U 182191712018409,1630078264917999,14617308518871210,131341152706852599

%N Expansion of (1-9x-27x^3)^(-1/3).

%F G.f.: g(x) = (1-9x-27x^3)^(-1/3).

%F D-finite diff. eq.: 3*(1-9x-27x^3)*g'(x) - (-1)*(-9-27x^2)*g(x) = 0. - _Georg Fischer_, Jan 15 2020

%F D-finite with recurrence: n*a(n) -3*(3*n-2)*a(n-1) -27*(n-2)*a(n-3)=0. - _Georg Fischer_, Jan 15 2020

%p f:= gfun:-rectoproc({a(0)=1, a(1)=3, a(2)=18, 1*(3*n-0)*a(n) + (-9)*(3*n-2)*a(n-1) + 0 + (-27)*(3*n-6)*a(n-3) = 0}, a(n), remember): map(f, [$0..30]); # from the differential equation - _Georg Fischer_, Jan 15 2020

%t CoefficientList[Series[(1-9x-27x^3)^(-1/3),{x,0,30}],x] (* _Harvey P. Dale_, Aug 22 2014 *)

%o (PARI) a(n)=polcoeff(1/(1-9*x-27*x^3)^(1/3)+O(x^(n+1)),n)

%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 20); Coefficients(R!( (1-9*x-27*x^3)^(-1/3))); // _Marius A. Burtea_, Jan 15 2020

%K nonn,easy

%O 0,2

%A _Benoit Cloitre_, Jun 05 2004

%E Offset 0 from _Georg Fischer_, Jan 15 2020

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)