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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). 5
1, 1, 4, 26, 226, 2395, 29278, 398499, 5899534, 93507783, 1569405110, 27672405800, 509622262860, 9759305238932, 193673399146066, 3972141366536794, 84010899306559470, 1829057795368804875, 40931310532585505770, 940322157062673670051, 22152626055397162566438 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 22 12:56 EDT 2021. Contains 345380 sequences. (Running on oeis4.)