OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(3*(n+1),n-k).
G.f.: B^3, where B is the g.f. of A144097.
a(n) ~ sqrt(8060 + 2651*sqrt(10)) * (223 + 70*sqrt(10))^n / (2 * sqrt(5*Pi) * n^(3/2) * 3^(3*n + 5/2)). - Vaclav Kotesovec, Nov 28 2024
PROG
(PARI) a(n) = sum(k=0, n, binomial(3*n+k+2, k)*binomial(3*(n+1), n-k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 20 2023
STATUS
approved