cp's OEIS Frontend

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.

%I A107098 #4 Mar 30 2012 18:36:46
%S A107098 0,1,2,2,3,0,13,-50,289,-1693,10736,-72091,510498,-3792518,29447687,
%T A107098 -238250274,2003475307,-17473865437,157785848332,-1472797717102,
%U A107098 14191079794761,-140977192451948,1442305028220567,-15180799919267781,164228909550516306,-1824477798876645279
%N 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.
%F A107098 G.f. A(x) = series-reversion of (G(-x)+x)/x where G(x) is g.f. for A030266.
%e A107098 Series reversion of g.f.:
%e A107098 x + 2*x^2 + 2*x^3 + 3*x^4 + 13*x^6 - 50*x^7 + 289*x^8 -+...
%e A107098 equals (G(-x)+x)/x where G(x) is g.f. for A030266:
%e A107098 x - 2*x^2 + 6*x^3 - 23*x^4 + 104*x^5 - 531*x^6 +-...
%o A107098 (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))}
%Y A107098 Cf. A107097, A030266.
%K A107098 sign
%O A107098 0,3
%A A107098 _Paul D. Hanna_, May 12 2005