OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-5*k,k) * binomial(3*n-6*k,n-2*k) / (2*n-4*k+1).
D-finite with recurrence 2*n*(2*n+1)*(3*n-7)*a(n) -3*(3*n-1)*(3*n-7)*(3*n-2) *a(n-1) -2*(n-3)*(18*n^2-33*n+4) *a(n-2) +2*(18*n^3-141*n^2+287*n-64) *a(n-4) -2*(n-4)*(3*n-1)*(2*n-13)*a(n-6)=0. - R. J. Mathar, Jul 27 2023
MAPLE
A364474 := proc(n)
add( binomial(3*n-5*k, k) * binomial(3*n-6*k, n-2*k)/(2*n-4*k+1), k=0..n/2) ;
end proc:
seq(A364474(n), n=0..80); # R. J. Mathar, Jul 27 2023
MATHEMATICA
Table[Sum[Binomial[3*n - 5*k, k]*Binomial[3*n - 6*k, n - 2*k]/(2*n - 4*k + 1), {k, 0, Floor[n/2]}], {n, 0, 25}] (* Wesley Ivan Hurt, May 25 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(3*n-5*k, k)*binomial(3*n-6*k, n-2*k)/(2*n-4*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 26 2023
STATUS
approved