A192407 A diagonal of square array A192404.

1, 4, 31, 291, 3092, 35839, 441925, 5721008, 77009425, 1071034612, 15319883964, 224628789200, 3368096726910, 51552652046550, 804490751228163, 12788591015038781, 206977224029107906, 3409582505289727239, 57165456138722305360

Offset: 1

Author

Paul D. Hanna, Jun 30 2011

Keywords

• nonn

Comments

The g.f. G(x,y) of square array A192404 satisfies the relations:

G(x,y) = 1 + Sum{n>=1} x^n*y*G(x,y)^n/(1 - y*G(x,y)^(2*n)),

G(x,y) = 1 + Sum{n>=1} y^n*x*G(x,y)^(2*n-1)/(1 - x*G(x,y)^(2*n-1)),

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.

Examples

			G.f.: A(x) = x + 4*x^2 + 31*x^3 + 291*x^4 + 3092*x^5 + 35839*x^6 +...
		

Crossrefs

Cf. A192404, A192405, A192406.

Programs

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)}

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)}