A168449 G.f. satisfies: A(x/A(x)) = C(x)^2 where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).

1, 2, 9, 60, 520, 5450, 65830, 886466, 13005906, 204607622, 3412713687, 59858823020, 1097439583778, 20934702108924, 414042879930671, 8466407067384676, 178587080601453990, 3878812336463745962

Offset: 0

Author

Paul D. Hanna, Dec 06 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 9*x^2 + 60*x^3 + 520*x^4 + 5450*x^5 +...
A(x/A(x)) = 1 + 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 132*x^5 + 429*x^6 +...
		

Crossrefs

Cf. A154677, A168448, A168479 (variant).

Programs

PARI

{a(n)=local(A=1+x, F=sum(k=0, n, binomial(2*k+1, k)/(2*k+1)*x^k)+x*O(x^n)); for(i=0, n, A=subst(F^2, x, serreverse(x/(A+x*O(x^n))))); polcoeff(A, n)}

PARI

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

Formula

G.f. satisfies: A(x) = [1 + A(x)*Series_Reversion(x/A(x))]^2.

G.f. satisfies: A( (x-x^2)/A(x-x^2) ) = 1/(1-x)^2.

G.f. satisfies: A( (x/(1+x)^2)/A(x/(1+x)^2)^2 ) = (1 + x)^2.

Self-convolution of A168448.