OFFSET
0,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: A(x) = -2*x / (1-sqrt(1+4*x*(1-x)^2)).
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(2*k-1,k) * binomial(2*(k-1),n-k)/(2*k-1).
MATHEMATICA
A363816[n_]:=(-1)^(n-1)Sum[Binomial[2k-1, k]Binomial[2(k-1), n-k]/(2k-1), {k, 0, n}]; Array[A363816, 30, 0] (* Paolo Xausa, Oct 20 2023 *)
PROG
(PARI) a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(2*(k-1), n-k)/(2*k-1));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Oct 18 2023
STATUS
approved