OFFSET
0,4
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(3*n,k) * binomial(n-k,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+x^3)^3 ). See A372377.
PROG
(PARI) a(n, s=3, t=3, u=-2) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 29 2024
STATUS
approved