OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-3*k,k) * binomial(3*n-4*k,n-2*k) / (2*n-2*k+1).
D-finite with recurrence 2*n*(2*n+1)*a(n) -(5*n+1)*(3*n-2)*a(n-1) +4*(-25*n^2+75*n-59) *a(n-2) +9*(-15*n^2+69*n-80)*a(n-3) -6*(3*n-8)*(3*n-10) *a(n-4)=0. - R. J. Mathar, Jul 27 2023
MAPLE
A364475 := proc(n)
add( binomial(3*n-3*k, k) * binomial(3*n-4*k, n-2*k)/(2*n-2*k+1), k=0..n/2) ;
end proc:
seq(A364475(n), n=0..80); # R. J. Mathar, Jul 27 2023
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(3*n-3*k, k)*binomial(3*n-4*k, n-2*k)/(2*n-2*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 26 2023
STATUS
approved