OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(3*n-3*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)^3 + x^3) ).
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n, k)*binomial(3*n-3*k, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 14 2024
STATUS
approved