OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = [x^n] 1/(1 - x^3 / (1 - x)^4)^n.
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1 - x^3 / (1 - x)^4) ). See A389350.
MATHEMATICA
Table[Sum[Binomial[n+k-1, k]Binomial[n+k-1, n-3*k], {k, 0, Floor[n/3]}], {n, 0, 40}] (* Vincenzo Librandi, Oct 03 2025 *)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n+k-1, k)*binomial(n+k-1, n-3*k));
(Magma) [&+[Binomial(n+k-1, k) * Binomial(n+k-1, n-3*k) : k in [0..Floor(n/3)] ]: n in [0..30]]; // Vincenzo Librandi, Oct 03 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 01 2025
STATUS
approved