A185898 G.f. satisfies: x + x^2 = A(x - A(x)^2).

1, 2, 8, 58, 516, 5264, 59056, 712002, 9091360, 121741316, 1697801200, 24533242088, 365899614704, 5615722652912, 88482403906752, 1428528355241602, 23595413088087220, 398214274587320432, 6859495185702804744

Offset: 1

Author

Paul D. Hanna, Feb 05 2011

Keywords

• nonn

Examples

			G.f.: A(x) = x + 2*x^2 + 8*x^3 + 58*x^4 + 516*x^5 + 5264*x^6 +...
Related expansions.
x - A(x)^2 = x - x^2 - 4*x^3 - 20*x^4 - 148*x^5 - 1328*x^6 -...
Let G(x) equal the series reversion of x - A(x)^2, then
G(x) = x + x^2 + 6*x^3 + 45*x^4 + 414*x^5 + 4310*x^6 + 49068*x^7 +...
G(x)^2 = x^2 + 2*x^3 + 13*x^4 + 102*x^5 + 954*x^6 + 9988*x^7 +...
		

Programs

PARI

{a(n)=local(A=x+2*x^2,B=serreverse(x*(1+x+x*O(x^n))));for(i=1,n,A=serreverse(B-subst(A,x,B)^2));polcoeff(A,n)}

Formula

G.f.: A(x) = G(x) + G(x)^2 where

* G(x) = (sqrt(1 + 4*A(x)) - 1)/2;

* G(x) = Series_Reversion(x - A(x)^2).