A382544 Expansion of 1/(1 - x/(1 - 9*x)^(1/3))^3.
1, 3, 15, 100, 753, 6006, 49456, 415422, 3536802, 30404161, 263271639, 2292524970, 20052238465, 176029542285, 1549916592645, 13681091072620, 121020187476717, 1072477163769417, 9519299301332377, 84609930915003882, 752947626436806021, 6707715814093174588
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
Programs
-
Magma
R
:= PowerSeriesRing(Rationals(), 25);f := x / (1 - 9*x)^(1/3);G := 1 / (1 - f)^3;Coefficients(G); // Vincenzo Librandi, Mar 31 2025 -
Mathematica
Table[Sum[9^(n-k)*Binomial[k+2,2]* Binomial [n-2*k/3-1, n-k],{k,0,n}],{n,0,25}] (* Vincenzo Librandi, Mar 31 2025 *) -
PARI
a(n) = sum(k=0, n, 9^(n-k)*binomial(k+2, 2)*binomial(n-2*k/3-1, n-k));
Formula
a(n) = Sum_{k=0..n} 9^(n-k) * binomial(k+2,2) * binomial(n-2*k/3-1,n-k).