OFFSET
0,5
FORMULA
G.f.: (1-x)*(sqrt(1+x^2+4*x^3)-sqrt(1+x^2))/(2*x^3*sqrt(1+x^2));
a(n) = Sum_{k=0..n} (-1)^binomial(n-k+1,2)*binomial(floor((n-k)/2),k)*A000108(k).
Conjecture: (n+3)*(n-2)*a(n) -4*a(n-1) +2*(n^2-n-4)*a(n-2) +2*(2*n^2-7*n+2)*a(n-3) +(n+1)*(n-4)*a(n-4) +2*(n-1)*(2*n-7)*a(n-5)=0. - R. J. Mathar, Nov 15 2012
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Feb 23 2009
EXTENSIONS
Divisor x^3 inserted in the g.f. - R. J. Mathar, Feb 06 2015
STATUS
approved