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%I #6 Mar 30 2012 18:37:27
%S 1,4,31,291,3092,35839,441925,5721008,77009425,1071034612,15319883964,
%T 224628789200,3368096726910,51552652046550,804490751228163,
%U 12788591015038781,206977224029107906,3409582505289727239,57165456138722305360
%N A diagonal of square array A192404.
%C The g.f. G(x,y) of square array A192404 satisfies the relations:
%C _ G(x,y) = 1 + Sum_{n>=1} x^n*y*G(x,y)^n/(1 - y*G(x,y)^(2*n)),
%C _ G(x,y) = 1 + Sum_{n>=1} y^n*x*G(x,y)^(2*n-1)/(1 - x*G(x,y)^(2*n-1)),
%C where G(x,y) = 1 + Sum_{n>=1,k>=1} A192404(n,k)*x^n*y^k, and this sequence consists of the diagonal terms a(n) = A192404(n+1,n) for n>=1.
%e G.f.: A(x) = x + 4*x^2 + 31*x^3 + 291*x^4 + 3092*x^5 + 35839*x^6 +...
%o (PARI) {a(n)=local(A=x*y);for(i=1,n+1,A=1+sum(m=1,n+1,x^m*y*A^m/(1-y*A^(2*m)+x*O(x^n)+y*O(y^n))));polcoeff(polcoeff(A,n+1,x),n,y)}
%o (PARI) {a(n)=local(A=x*y);for(i=1,n+1,A=1+sum(m=1,n+1,y^m*x*A^(2*m-1)/(1-x*A^(2*m-1)+x*O(x^n)+y*O(y^n))));polcoeff(polcoeff(A,n,y),n+1,x)}
%Y Cf. A192404, A192405, A192406.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Jun 30 2011
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