OFFSET
0,2
FORMULA
G.f.: A(x) = 1/(-2*x*(1+x) + sqrt(1+(2*x*(1+x))^2)).
a(n) = Sum_{k=0..n} 4^k * binomial(k/2+1/2,k) * binomial(k,n-k)/(k+1).
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(1/(-2*x*(1+x)+sqrt(1+(2*x*(1+x))^2)))
(PARI) a(n) = sum(k=0, n, 4^k*binomial(k/2+1/2, k)*binomial(k, n-k)/(k+1));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 16 2024
STATUS
approved