OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..984
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(4*n-4*k+2,n-k).
D-finite with recurrence 3*(3*n+2)*(3*n+1)*(n+1)*a(n) +4*(-91*n^3 -32*n^2 +n+2)*a(n-1) +2*(n-1)*(465*n^2 -337*n+86)*a(n-2) -4*(n-1)*(n-2) *(219*n-187)*a(n-3) +283*(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Jan 28 2024
MAPLE
A369617 := proc(n)
add(binomial(n+1, k) * binomial(4*n-4*k+2, n-k), k=0..n) ;
%/(n+1) ;
end proc;
seq(A369617(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)^3+x))/x)
(PARI) a(n) = sum(k=0, n, binomial(n+1, k)*binomial(4*n-4*k+2, n-k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 27 2024
STATUS
approved