A195154 G.f. A(x) satisfies: A(A(x)) = (1+x-x^2)*A(x).

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

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+x-x^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+x-x^2) ))/2); A=round(A)); polcoeff(A, n, x))}

Crossrefs

Cf. A195440, A107095.

Sequence in context: A293653 A246541 A112385 * A353995 A353982 A340243

Adjacent sequences: A195151 A195152 A195153 * A195155 A195156 A195157

Keyword

sign

Author

Paul D. Hanna, Sep 23 2011

Status

approved