OFFSET
0,5
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(3*k,k) * binomial(n-k-1,n-2*k) / (2*k+1).
D-finite with recurrence 8*n*(n+1)*a(n) -28*n*(n-1)*a(n-1) +2*(-9*n^2-n+14)*a(n-2) +(115*n^2-463*n+426)*a(n-3) +4*(-26*n^2+168*n-265)*a(n-4) +3*(3*n-13)*(3*n-14)*a(n-5)=0. - R. J. Mathar, Sep 26 2024
MAPLE
A376489 := proc(n)
add(binomial(3*k, k)*binomial(n-k-1, n-2*k)/(2*k+1), k=0..floor(n/2)) ;
end proc:
seq(A376489(n), n=0..70) ; # R. J. Mathar, Sep 26 2024
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(3*k, k)*binomial(n-k-1, n-2*k)/(2*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 25 2024
STATUS
approved