A168448 G.f. satisfies: A(x/A(x)^2) = C(x) where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).

1, 1, 4, 26, 226, 2395, 29278, 398499, 5899534, 93507783, 1569405110, 27672405800, 509622262860, 9759305238932, 193673399146066, 3972141366536794, 84010899306559470, 1829057795368804875, 40931310532585505770, 940322157062673670051, 22152626055397162566438

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

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

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

Example

G.f.: A(x) = 1 + x + 4*x^2 + 26*x^3 + 226*x^4 + 2395*x^5 +...
A(x/A(x)^2) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...

Prog

(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, x, serreverse(x/(A+x*O(x^n))^2))); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+A^2*serreverse(x/(A+x*O(x^n))^2)); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A154677, A168449.

Sequence in context: A245768 A152407 A291847 * A105616 A293915 A107879

Adjacent sequences: A168445 A168446 A168447 * A168449 A168450 A168451

Keyword

nonn

Author

Paul D. Hanna, Dec 06 2009

Status

approved