OFFSET
0,2
FORMULA
G.f.: sqrt( (1-2*x)/(1-6*x) ).
n*a(n) = 2*(4*n-3)*a(n-1) - 12*(n-2)*a(n-2).
Sum_{i=0..n} Sum_{j=0..i} (1/2)^i * a(j) * a(i-j) = 3^n.
a(n) = 2 * A005573(n-1) for n > 0.
a(n) ~ 2^(n + 1/2) * 3^(n - 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Feb 04 2023
PROG
(PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(n-1, n-k)*binomial(2*k, k));
(PARI) my(N=30, x='x+O('x^N)); Vec(sqrt((1-2*x)/(1-6*x)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 03 2023
STATUS
approved