OFFSET
0,2
FORMULA
a(n) = -4^n*binomial(n/2,n)/(n/2 - 1), except a(2) = 8, for n>=0.
G.f.: (exp(asinh(2*x)))^2. - Philippe Deléham, Feb 01 2012
D-finite with recurrence: (-n+1)*a(n) +(-n+2)*a(n-1) +4*(-n+4)*a(n-2) +4*(-n+5)*a(n-3)=0. - R. J. Mathar, Jan 23 2020
From Alexander Burstein, Mar 27 2022: (Start)
G.f. satisfies: A(-x) = 1/A(x).
a(2*n+3) = (-1)^n*8*A000108(n) for n>=0. (End)
PROG
(PARI) a(n)=4^n*if(n==2, 1/2, binomial(n/2, n)/(1-n/2))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Dec 02 2007
STATUS
approved