A192406 Main diagonal of square array A192404, with a(0)=1.

1, 1, 2, 14, 114, 1131, 12393, 146712, 1838094, 24088842, 327526513, 4593918125, 66198455671, 977113573208, 14741071612583, 226941948201964, 3561383719180100, 56926946565867437, 926444637518092848, 15347533201937448776, 258809102457332568964

Offset

0,3

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,n); what then is the g.f. of this sequence?

Links

Table of n, a(n) for n=0..20.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 14*x^3 + 114*x^4 + 1131*x^5 + 12393*x^6 +...

Prog

(PARI) {a(n)=local(A=1+x*y); for(i=1, n, A=1+sum(m=1, n, x^m*y*A^m/(1-y*A^(2*m)+x*O(x^n)+y*O(y^n)))); polcoeff(polcoeff(A, n, x), n, y)}
(PARI) {a(n)=local(A=1+x*y); for(i=1, n, A=1+sum(m=1, n, 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, x)}

Crossrefs

Cf. A192404, A192405, A192407.

Sequence in context: A199649 A357584 A216581 * A332664 A092639 A231615

Adjacent sequences: A192403 A192404 A192405 * A192407 A192408 A192409

Keyword

nonn

Author

Paul D. Hanna, Jun 30 2011

Status

approved