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

1,2

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.

Links

Table of n, a(n) for n=1..19.

Example

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

Prog

(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)}

Crossrefs

Cf. A192404, A192405, A192406.

Sequence in context: A265949 A081054 A261053 * A000858 A003436 A307504

Adjacent sequences: A192404 A192405 A192406 * A192408 A192409 A192410

Keyword

nonn

Author

Paul D. Hanna, Jun 30 2011

Status

approved