A383584 a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k-1,k) * binomial(k,n-4*k).

1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 0, 3, 12, 10, 0, 4, 30, 60, 35, 5, 60, 210, 280, 132, 105, 560, 1260, 1267, 630, 1260, 4200, 6938, 5796, 4236, 11550, 27729, 36396, 28644, 34155, 90100, 168663, 188100, 163020, 276573, 631290, 973830, 995280, 1068222, 2111252, 4104100

Offset: 0

Author

Seiichi Manyama, May 01 2025

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A005717, A383583.

Cf. A383572.

Programs

Magma

[&+[Binomial(n-3*k-1,k) * Binomial(k,n-4*k): k in [0..Floor(n div 4)]]: n in [0..45]]; // Vincenzo Librandi, May 02 2025

Mathematica

Table[Sum[Binomial[n-3*k-1,k]* Binomial[k,n-4*k],{k,0,Floor[n/4]}],{n,0,40}] (* Vincenzo Librandi, May 02 2025 *)

PARI

a(n) = sum(k=0, n\4, binomial(n-3*k-1, k)*binomial(k, n-4*k));

Formula

G.f.: (1/2) * ( 1 + 1/sqrt(1 - 4*x^5/(1-x^4)^2) ).