A195440 G.f. satisfies: A(x - x*A(x) - x*A(x)^2) = x.

1, 1, 4, 21, 134, 968, 7662, 65135, 587040, 5559342, 54965230, 564651110, 6004908296, 65920345700, 745289233564, 8661959227407, 103330815828292, 1263608418272768, 15823268263301680, 202712359166886406, 2654710188935753950, 35514167158635839770

Offset: 1

Author

Paul D. Hanna, Sep 18 2011

Keywords

• nonn

Comments

Compare to g.f. C(x) of the Catalan numbers: C(x - x*C(x) + x*C(x)^2) = x.

Examples

			G.f.: A(x) = x + x^2 + 4*x^3 + 21*x^4 + 134*x^5 + 968*x^6 + 7662*x^7 +...
Related expansions.
A(x)^2 = x^2 + 2*x^3 + 9*x^4 + 50*x^5 + 326*x^6 + 2372*x^7 + 18773*x^8 +...
A(x) + A(x)^2 = x + 2*x^2 + 6*x^3 + 30*x^4 + 184*x^5 + 1294*x^6 +...
where the series reversion of A(x) begins:
x-x*A(x)-x*A(x)^2 = x - x^2 - 2*x^3 - 6*x^4 - 30*x^5 - 184*x^6 - 1294*x^7 - 10034*x^8 +...
		

Crossrefs

Cf. A000108 (Catalan numbers).

Programs

PARI

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