OFFSET
0,3
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1 / sqrt(1+4*x^2/(1-x)).
n*a(n) = 2*(n-1)*a(n-1) - (5*n-6)*a(n-2) + 2*(2*n-5)*a(n-3).
MATHEMATICA
RecurrenceTable[{a[0]==1, a[1]==0, a[2]==-2, a[n]==1/n (2(n-1)a[n-1]-(5n-6)a[n-2]+2(2n-5)a[n-3])}, a, {n, 40}] (* Harvey P. Dale, Sep 20 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n-1-k, n-2*k)*binomial(2*k, k));
(PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1+4*x^2/(1-x)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 03 2023
STATUS
approved