A228863 - OEIS

%I #5 Sep 05 2013 21:13:18

%S 1,-1,1,-2,3,-4,6,-10,18,-35,71,-147,303,-616,1244,-2508,5067,-10296,

%T 21097,-43624,90929,-190629,401053,-845374,1784015,-3768964,7973941,

%U -16902610,35909941,-76473042,163227753,-349117291,748032779,-1605215441,3449280634,-7420879949,15984045722

%N Series reversion of the g.f. of A228862.

%C The g.f. of A228862, F(x), satisfies: x = F(x - F(x^2 - F(x^3 - F(x^4 - F(x^5 -...)))).

%H Paul D. Hanna, <a href="/A228863/b228863.txt">Table of n, a(n) for n = 1..300</a>

%F G.f.: A(x) = x - F(x^2 - F(x^3 - F(x^4 - F(x^5 -...))), where F(x) is the g.f. of A228862.

%e G.f.: A(x) = x - x^2 + x^3 - 2*x^4 + 3*x^5 - 4*x^6 + 6*x^7 - 10*x^8 + 18*x^9 +...

%e where

%e A(x - A(x)) = x^2 - x^3 + x^4 - x^5 + x^7 - x^8 + x^10 - x^11 + 3*x^13 +...

%e A(x^2 - A(x - A(x))) = x^3 - x^4 + x^5 - x^6 + x^7 - 2*x^8 + 3*x^9 - 3*x^10 +...

%e A(x^3 - A(x^2 - A(x - A(x)))) = x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^11 +...

%e A(x^4 - A(x^3 - A(x^2 - A(x - A(x))))) = x^5 - x^6 + x^7 - x^8 + x^9 - x^10 +...

%e ...

%e The series reversion of A(x) is the g.f. of A228862, which begins:

%e F(x) = x + x^2 + x^3 + 2*x^4 + 5*x^5 + 11*x^6 + 24*x^7 + 58*x^8 + 146*x^9 +...

%o (PARI) {a(n)=local(A=x+x^2,G=x^(n+1));for(i=1,n+1,A=serreverse(x-G+x^2*O(x^n));G=x^(n+1);for(k=0,n-1,G=subst(A,x,x^(n-k+1)-G+x^2*O(x^n))));polcoeff(serreverse(A),n)}

%o for(n=1,40,print1(a(n),", "))

%K sign

%O 1,4

%A _Paul D. Hanna_, Sep 05 2013