OFFSET
0,4
COMMENTS
Hankel transform is A160566(n+1).
a(0)=1 followed by A025252. [From R. J. Mathar, May 20 2009]
FORMULA
G.f.: (1-x^2-sqrt(1-2x^2-8x^3+x^4))/(4x^3);
G.f.: 1/(1-x^2-2*x^3/(1-x^2-2*x^3/(1-x^2-2*x^3/(1-x^2-2*x^3/(1-... (continued fraction).
a(n)=sum{k=0..floor(n/2), C(n-k,2n-4k)*2^(n-2k)*A000108(n-2k)};
a(n)=sum{k=0..n, C(n-k/2,2(n-k))*2^(n-k)*A000108(n-k)*(1+(-1)^k)/2};
a(n)=sum{k=0..n, C((n+k)/2,2k)*2^k*A000108(k)(1+(-1)^(n-k))/2}.
G.f.: (1/(1-x^2))c(2x^3/(1-x^2)^2) where c(x) is the g.f. of A000108. [From Paul Barry, May 20 2009]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 19 2009
STATUS
approved