OFFSET
0,3
COMMENTS
Derived from central terms of triangle: a(n) = A125278(2*n,n)/(n+1).
FORMULA
G.f. satisfies: A(x) = 1 + x*A(x)^2 * A( x^2*A(x)^4/(A(x) - 1) ). By definition, G.f. satisfies: A(x) = 1 + G(x*A(x)^2); G(x*A(x)) = x*A(x)^2; x*A(x^2/G(x)) = G(x); where G(x) = x + x*G(G(x)) is g.f. of A030266.
EXAMPLE
A(x) = 1 + x + 3*x^2 + 13*x^3 + 68*x^4 + 400*x^5 + 2555*x^6 +...
The g.f. of A030266 is G(x) = x + x*G(G(x)) where
G(x) = x + x^2 + 2*x^3 + 6*x^4 + 23*x^5 + 104*x^6 + 531*x^7 + 2982*x^8+..
PROG
(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+x*A^2*subst(A, x, x^2*A^4/(A-1+x^2*O(x^n)))); polcoeff(A, n, x)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 26 2006
STATUS
approved