

A195154


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


0



1, 1, 2, 6, 30, 184, 1294, 10034, 83908, 746006, 6983600, 68360302, 696122684, 7345561204, 80074813040, 899590031932, 10394864935860, 123344285904634, 1500938535372826, 18709376854618500, 238664936823622052, 3113060999816038350
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..22.


FORMULA

The series reversion of A(x) is G(x) where G(x) is the g.f. of A195440, which satisfies: G(x  x*G(x)  x*G(x)^2) = x.


EXAMPLE

G.f.: A(x) = x + x^2  2*x^3 + 6*x^4  30*x^5 + 184*x^6  1294*x^7 +...
where A(A(x)) = (1+xx^2)*A(x) begins:
A(A(x)) = x + 2*x^2  2*x^3 + 3*x^4  22*x^5 + 148*x^6  1080*x^7 +...
The series reversion of A(x) begins:
G(x) = x  x^2 + 4*x^3  21*x^4 + 134*x^5  968*x^6 + 7662*x^7 +...
where G(x) is the g.f. of A195440.


PROG

(PARI) {a(n)=local(A, B, F); if(n<1, 0, F=x+x^2+x*O(x^n); A=F;
for(j=0, n, for(i=0, j, B=serreverse(A); A=(A+subst(B, x, A*(1+xx^2) ))/2); A=round(A)); polcoeff(A, n, x))}


CROSSREFS

Cf. A195440, A107095.
Sequence in context: A293653 A246541 A112385 * A078700 A176719 A203000
Adjacent sequences: A195151 A195152 A195153 * A195155 A195156 A195157


KEYWORD

sign


AUTHOR

Paul D. Hanna, Sep 23 2011


STATUS

approved



