OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(3*n-3*k+1,n-k).
D-finite with recurrence 2*(n+1)*(2*n+1)*a(n) +3*(-13*n^2+1)*a(n-1) +33*(2*n-1)*(n-1)*a(n-2) -31*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Jan 28 2024
MAPLE
A369616 := proc(n)
add(binomial(n+1, k) * binomial(3*n-3*k+1, n-k), k=0..n) ;
%/(n+1) ;
end proc;
seq(A369616(n), n=0..70) ; # R. J. Mathar, Jan 28 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)^2+x))/x)
(PARI) a(n) = sum(k=0, n, binomial(n+1, k)*binomial(3*n-3*k+1, n-k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 27 2024
STATUS
approved