cp's OEIS Frontend

A104495 Matrix inverse of triangle A099602, read by rows, where row n of A099602 equals the inverse binomial transform of column n of the triangle of trinomial coefficients (A027907).

%I A104495 #5 Mar 30 2012 18:36:45
%S A104495 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,
%T A104495 -8,1,-1,7,-294,149,-124,40,-10,1,1,-8,919,-443,448,-164,61,-11,1,-1,
%U A104495 9,-2974,1362,-1576,612,-298,72,-13,1,1,-10,9891,-4336,5510,-2188,1294,-370,99,-14,1,-1,11,-33604,14227,-19322,7698
%N A104495 Matrix inverse of triangle A099602, read by rows, where row n of A099602 equals the inverse binomial transform of column n of the triangle of trinomial coefficients (A027907).
%C A104495 Row sums are A104496. Absolute row sums form A014137 (partial sums of Catalan numbers). Column 2 is signed A014143.
%F A104495 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).
%e A104495 Rows begin:
%e A104495 1;
%e A104495 -1,1;
%e A104495 1,-2,1;
%e A104495 -1,3,-4,1;
%e A104495 1,-4,12,-5,1;
%e A104495 -1,5,-34,17,-7,1;
%e A104495 1,-6,98,-51,32,-8,1;
%e A104495 -1,7,-294,149,-124,40,-10,1;
%e A104495 1,-8,919,-443,448,-164,61,-11,1;
%e A104495 -1,9,-2974,1362,-1576,612,-298,72,-13,1; ...
%o A104495 (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)}
%Y A104495 Cf. A099602, A027907, A000108, A104496, A014137, A014143.
%K A104495 sign,tabl
%O A104495 0,5
%A A104495 _Paul D. Hanna_, Mar 11 2005