A298308 Expansion of (9*x^3+9*x+1)^(1/3).

1, 3, -9, 48, -288, 1917, -13563, 99927, -758079, 5879754, -46401687, 371336886, -3005973612, 24568135839, -202441986099, 1679863711851, -14024710539684, 117715876380531, -992724682487382, 8407187391492162, -71467928398473984, 609605247759545934, -5215842747304421544, 44752623977413097928, -384969343166207926893

Offset: 0

Author

Robert Israel, Jan 16 2018

Keywords

• sign

Examples

			(9*x^3+9*x+1)^(1/3) = 1+3*x-9*x^2+48*x^3-288*x^4+1917*x^5+...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..1046

Programs

Maple

f:= gfun:-rectoproc({(-9+9*n)*a(n)+(15+9*n)*a(n+2)+(n+3)*a(n+3), a(0) = 1, a(1) = 3, a(2) = -9},a(n),remember):
map(f, [$0..30]);

Mathematica

CoefficientList[Series[(9*x^3 + 9*x + 1)^(1/3), {x, 0, 25}], x] (* Wesley Ivan Hurt, Jan 20 2024 *)

Formula

G.f.: (9*x^3+9*x+1)^(1/3).

D-finite with recurrence: (-9+9*n)*a(n)+(15+9*n)*a(n+2)+(n+3)*a(n+3) = 0.

a(n) = Gamma(4/3)*Sum_{0<=j<=n/3} 9^(n-2*j)/(Gamma(4/3-n+2*j)*(n-3*j)!*j!).