OFFSET
0,2
COMMENTS
Diagonal of rational function 1/(1 - x - y + x^4*y^3). - Seiichi Manyama, Mar 23 2023
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1/sqrt(1 - 4*x*(1 - x^3)).
n*a(n) = 2*(2*n-1)*a(n-1) - 2*(2*n-4)*a(n-4).
MAPLE
A360219 := proc(n)
add((-1)^k*binomial(n-3*k, k)*binomial(2*(n-3*k), n-3*k), k=0..n/3) ;
end proc:
seq(A360219(n), n=0..70) ; # R. J. Mathar, Mar 12 2023
PROG
(PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(n-3*k, k)*binomial(2*(n-3*k), n-3*k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x*(1-x^3)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 31 2023
STATUS
approved