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

1, 3, 18, 135, 1053, 8505, 70470, 594135, 5073840, 43761870, 380433024, 3328474032, 29276671347, 258669163665, 2294194659012, 20415148177023, 182191712018409, 1630078264917999, 14617308518871210, 131341152706852599

Offset

0,2

Links

Table of n, a(n) for n=0..19.

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

Sequence in context: A251733 A355103 A355105 * A114178 A005159 A151383

Adjacent sequences: A095773 A095774 A095775 * A095777 A095778 A095779

Keyword

nonn,easy

Author

Benoit Cloitre, Jun 05 2004

Extensions

Offset 0 from Georg Fischer, Jan 15 2020

Status

approved