OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(4*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)^2) ). See A369485.
PROG
(PARI) a(n, s=3, t=2, 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, Feb 11 2024
STATUS
approved