A383604 Expansion of 1/( (1-x)^2 * (1-x-9*x^3) )^(1/3).
1, 1, 1, 4, 7, 10, 31, 70, 127, 328, 799, 1666, 4000, 9817, 22078, 52060, 126727, 296101, 699601, 1691350, 4024450, 9574393, 23081776, 55394488, 132650923, 319807159, 770872429, 1855190146, 4479086230, 10825202521, 26145137668, 63241928080, 153144714331
Offset: 0
Keywords
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..500
Programs
-
Magma
R
:=PowerSeriesRing(Rationals(), 35); Coefficients(R!( 1/( (1-x)^2 * (1-x-9*x^3) )^(1/3))); // Vincenzo Librandi, May 06 2025 -
Mathematica
CoefficientList[Series[1/((1-x)^2*(1-x-9*x^3))^(1/3),{x,0,32}],x] (* Stefano Spezia, May 02 2025 *) Table[Sum[(-9)^k*Binomial[-1/3,k]*Binomial[n-2*k,k],{k,0,Floor[n/3]}],{n,0,35}] (* Vincenzo Librandi, May 06 2025 *) -
PARI
a(n) = sum(k=0, n\3, (-9)^k*binomial(-1/3, k)*binomial(n-2*k, k));
Formula
a(n) = Sum_{k=0..floor(n/3)} (-9)^k * binomial(-1/3,k) * binomial(n-2*k,k).