A386006 a(n) = Sum_{k=0..n} binomial(3*n-2,k).
1, 2, 11, 64, 386, 2380, 14893, 94184, 600370, 3850756, 24821333, 160645504, 1043243132, 6794414896, 44360053772, 290244832992, 1902631226010, 12493030680180, 82153313341429, 540953389469312, 3566279609565226, 23536562549993228, 155489358646406149
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Programs
-
Magma
[&+[Binomial(3*n-2,k): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Aug 27 2025
-
Mathematica
Table[Sum[Binomial[3*n-2,k],{k,0,n}],{n,0,25}] (* Vincenzo Librandi, Aug 27 2025 *) -
PARI
a(n) = sum(k=0, n, binomial(3*n-2, k));
Formula
a(n) = [x^n] (1+x)^(3*n-2)/(1-x).
a(n) = [x^n] 1/((1-x)^(2*n-2) * (1-2*x)).
a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(3*n-2,k) * binomial(3*n-k-3,n-k).
a(n) = Sum_{k=0..n} 2^k * binomial(3*n-k-3,n-k).
G.f.: 1/(g * (2-g) * (3-2*g)) where g = 1+x*g^3 is the g.f. of A001764.