OFFSET
0,2
COMMENTS
Hankel transform of e.g.f. Bessel_I(0,2*sqrt(-1)*x) or (1,0,-2,0,6,0,-20,...).
Hankel transform of Sum_{k=0..n} (-1)^(n-k)*C(n,k)^2.
Hankel transform of A098331.
Hankel transform of A082590. - Paul Barry, Apr 26 2009
LINKS
FORMULA
G.f.: (1-2*x)/(1+4*x^2).
a(n) = 2^n*(cos(Pi*(n+1)/2)+sin(Pi*(n+1)/2)).
a(0) = 1, a(1) = -2, a(n) = -4*a(n-2). - Harvey P. Dale, Oct 12 2011
a(n) = ( 2*i^(n+1) )^n, where i = sqrt(-1). - Bruno Berselli, Oct 12 2011
E.g.f.: cos(2*x) - sin(2*x). - Arkadiusz Wesolowski, Aug 31 2012
From Amiram Eldar, Feb 17 2026: (Start)
Sum_{n>=0} 1/a(n) = 2/5.
Sum_{n>=0} (-1)^n/a(n) = 6/5. (End)
MATHEMATICA
LinearRecurrence[{0, -4}, {1, -2}, 40] (* or *) CoefficientList[ Series[ (1-2x)/(1+4x^2), {x, 0, 40}], x] (* Harvey P. Dale, Oct 12 2011 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Barry, Jun 17 2006
STATUS
approved