A107095 -id:A107095 - cp's OEIS frontend

A107096 G.f. A(x) satisfies: A(x)^2 = xG(x) where G(G(x)) = (1+x)^2G(x) and G(x) is the g.f. of A107095.

0, 1, 1, -2, 11, -88, 869, -9876, 124473, -1701630, 24870695, -384795184, 6257294780, -106377162620, 1882982975521, -34593496243070, 657935674477431, -12927331575084846, 261951066040220637, -5466177185459699916, 117315664923801661485, -2586804284853871362408

Offset: 0

Paul D. Hanna, May 12 2005

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Cf. A107095.

{a(n)=local(A,B,F);if(n<1,0,F=x+2*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)^2))/2); A=round(A));polcoeff(sqrt(x*A),n,x))}

{a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+serreverse(x*subst(A^2,x,x+x*O(x^n))));polcoeff(x*A,n)} \\ Paul D. Hanna, Mar 15 2010

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

G.f. satisfies: A(x) = x + x*Series_Reversion( A(x)^2/x ). - Paul D. Hanna, Mar 15 2010

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

Original entry on oeis.org

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

Offset: 1

Paul D. Hanna, Sep 23 2011

sign

			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.

Cf. A195440, A107095.

{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))}

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.

cp's OEIS Frontend

A107096 G.f. A(x) satisfies: A(x)^2 = xG(x) where G(G(x)) = (1+x)^2G(x) and G(x) is the g.f. of A107095.

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

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cp's OEIS Frontend

A107096 G.f. A(x) satisfies: A(x)^2 = x*G(x) where G(G(x)) = (1+x)^2*G(x) and G(x) is the g.f. of A107095.

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PARI

PARI

Formula

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

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Formula

A107096 G.f. A(x) satisfies: A(x)^2 = xG(x) where G(G(x)) = (1+x)^2G(x) and G(x) is the g.f. of A107095.