A107098 The self-COMPOSE transform of A107097 and also the partial sums of A107097: g.f. A(x) = G(G(x)) = G(x)/(1-x) where G(x) is the g.f. of A107097.

0, 1, 2, 2, 3, 0, 13, -50, 289, -1693, 10736, -72091, 510498, -3792518, 29447687, -238250274, 2003475307, -17473865437, 157785848332, -1472797717102, 14191079794761, -140977192451948, 1442305028220567, -15180799919267781, 164228909550516306, -1824477798876645279

Offset: 0

Author

Paul D. Hanna, May 12 2005

Keywords

• sign

Examples

			Series reversion of g.f.:
x + 2*x^2 + 2*x^3 + 3*x^4 + 13*x^6 - 50*x^7 + 289*x^8 -+...
equals (G(-x)+x)/x where G(x) is g.f. for A030266:
x - 2*x^2 + 6*x^3 - 23*x^4 + 104*x^5 - 531*x^6 +-...
		

Crossrefs

Cf. A107097, A030266.

Programs

PARI

{a(n)=local(A,B,F);if(n<1,0,F=x+2*x^2-3*x^3+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); A=round(A));polcoeff(A/(1-x),n,x))}

Formula

G.f. A(x) = series-reversion of (G(-x)+x)/x where G(x) is g.f. for A030266.