A214768 G.f. satisfies: A(x) = 1/A(-x*A(x)^8).

1, 2, 18, 180, 1734, 18300, 270420, 5151720, 96203910, 1565102844, 22108977596, 287976684088, 3835267955036, 55283720348664, 804522994149032, 10849701753955856, 150403977728200774, 3086256025416536700, 91156710989444409004, 2687925748932854737432

Offset: 0

Author

Paul D. Hanna, Jul 29 2012

Keywords

• nonn

Comments

Compare to: W(x) = 1/W(-x*W(x)^8) when W(x) = Sum_{n>=0} (4*n+1)^(n-1)*x^n/n!.

An infinite number of functions G(x) satisfy (*) G(x) = 1/G(-x*G(x)^8); for example, (*) is satisfied by G(x) = W(m*x), where W(x) = Sum_{n>=0} (4*n+1)^(n-1)*x^n/n!.

Examples

			G.f.: A(x) = 1 + 2*x + 18*x^2 + 180*x^3 + 1734*x^4 + 18300*x^5 + 270420*x^6 +...
A(x)^8 = 1 + 16*x + 256*x^2 + 3904*x^3 + 56320*x^4 + 793984*x^5 + 11567104*x^6 +...
		

Crossrefs

Cf. A214761, A214762, A214763, A214764, A214765, A214766, A214767, A214769.

Programs

PARI

{a(n)=local(A=1+2*x);for(i=0,n,A=(A+1/subst(A,x,-x*A^8+x*O(x^n)))/2);polcoeff(A,n)}
for(n=0,31,print1(a(n),", "))

Formula

The g.f. of this sequence is the limit of the recurrence:

(*) G_{n+1}(x) = (G_n(x) + 1/G_n(-x*G_n(x)^8))/2 starting at G_0(x) = 1+2*x.