OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(n-2*k,k) * binomial(2*(n-2*k),n-2*k).
n*a(n) = 2*(2*n-1)*a(n-1) + 4*(2*n-3)*a(n-3).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x-8*x^3))
(PARI) a(n) = sum(k=0, n\3, 2^k*binomial(n-2*k, k)*binomial(2*(n-2*k), n-2*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 13 2024
STATUS
approved