OFFSET
0,2
FORMULA
G.f.: g(x) = (1-9x-27x^3)^(-1/3).
D-finite diff. eq.: 3*(1-9x-27x^3)*g'(x) - (-1)*(-9-27x^2)*g(x) = 0. - Georg Fischer, Jan 15 2020
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
MAPLE
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
MATHEMATICA
CoefficientList[Series[(1-9x-27x^3)^(-1/3), {x, 0, 30}], x] (* Harvey P. Dale, Aug 22 2014 *)
PROG
(PARI) a(n)=polcoeff(1/(1-9*x-27*x^3)^(1/3)+O(x^(n+1)), n)
(Magma) R<x>:=PowerSeriesRing(Rationals(), 20); Coefficients(R!( (1-9*x-27*x^3)^(-1/3))); // Marius A. Burtea, Jan 15 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Jun 05 2004
EXTENSIONS
Offset 0 from Georg Fischer, Jan 15 2020
STATUS
approved