OFFSET
0,2
FORMULA
a(n) = binomial(n+2,2) - Sum_{k=0..n-1} a(k) * a(n-k-1).
G.f. A(x) satisfies A(x) = 1/(1-x)^3 - x * A(x)^2.
G.f.: 2 / ( (1-x)^3 * (1 + sqrt( 1 + 4*x/(1-x)^3 )) ).
D-finite with recurrence (n+1)*a(n) -2*a(n-1) +2*(n-3)*a(n-2) +4*(-n+2)*a(n-3) +(n-3)*a(n-4)=0. - R. J. Mathar, Jan 25 2023
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+2*k+2, n-k)*binomial(2*k, k)/(k+1));
(PARI) my(N=50, x='x+O('x^N)); Vec(2/((1-x)^3*(1+sqrt(1+4*x/(1-x)^3))))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jan 23 2023
STATUS
approved