A383599 Expansion of 1/( (1-x^3)^2 * (1-x^3-9*x) )^(1/3).

1, 3, 18, 127, 951, 7425, 59473, 484902, 4005720, 33425587, 281152551, 2380227705, 20259341335, 173218395228, 1486747223136, 12803424371263, 110579924167533, 957494150283249, 8309596928695417, 72260720257071936, 629526082305028041, 5493357757059584986

Offset: 0

Author

Seiichi Manyama, May 01 2025

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A383597, A383598.

Cf. A376806.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/( (1-x^3)^2 * (1-x^3-9*x) )^(1/3))); // Vincenzo Librandi, May 04 2025

Mathematica

Table[Sum[(-9)^(n-3*k)* Binomial[-1/3, n-3*k]* Binomial[n-2*k,k],{k,0,Floor[n/3]}],{n,0,22}] (* Vincenzo Librandi, May 04 2025 *)

PARI

a(n) = sum(k=0, n\3, (-9)^(n-3*k)*binomial(-1/3, n-3*k)*binomial(n-2*k, k));

Formula

a(n) = Sum_{k=0..floor(n/3)} (-9)^(n-3*k) * binomial(-1/3,n-3*k) * binomial(n-2*k,k).