login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A192407 A diagonal of square array A192404. 2
1, 4, 31, 291, 3092, 35839, 441925, 5721008, 77009425, 1071034612, 15319883964, 224628789200, 3368096726910, 51552652046550, 804490751228163, 12788591015038781, 206977224029107906, 3409582505289727239, 57165456138722305360 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 19 23:27 EDT 2021. Contains 345154 sequences. (Running on oeis4.)