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 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

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Last modified December 9 06:02 EST 2023. Contains 367685 sequences. (Running on oeis4.)