OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(3*n-3*k-1,n-3*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^2 / (1+x^3) ). See A369265.
PROG
(PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((u+1)*n-s*k-1, n-s*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 13 2024
STATUS
approved