OFFSET
0,5
COMMENTS
FORMULA
G.f.: A(x, y) = (1 + x*y/(1+x))/(1+x - x^2*y^2*Catalan(-x)^2), also G.f.: Column_k(x) = Catalan(-x)^(2*[k/2])/(1+x)^[(k+3)/2], where Catalan(x)=(1-(1-4*x)^(1/2))/(2*x) (cf. A000108).
EXAMPLE
Rows begin:
1;
-1,1;
1,-2,1;
-1,3,-4,1;
1,-4,12,-5,1;
-1,5,-34,17,-7,1;
1,-6,98,-51,32,-8,1;
-1,7,-294,149,-124,40,-10,1;
1,-8,919,-443,448,-164,61,-11,1;
-1,9,-2974,1362,-1576,612,-298,72,-13,1; ...
PROG
(PARI) {T(n, k)=local(X=x+x*O(x^n), Y=y+y*O(y^k)); polcoeff(polcoeff( (1+X*Y/(1+X))/(1+X-Y^2*(1-(1+4*X)^(1/2))^2/4), n, x), k, y)}
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Paul D. Hanna, Mar 11 2005
STATUS
approved