OFFSET
1,4
COMMENTS
The g.f. of A228862, F(x), satisfies: x = F(x - F(x^2 - F(x^3 - F(x^4 - F(x^5 -...))))).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..300
FORMULA
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.
EXAMPLE
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 +...
where
A(x - A(x)) = x^2 - x^3 + x^4 - x^5 + x^7 - x^8 + x^10 - x^11 + 3*x^13 +...
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 +...
A(x^3 - A(x^2 - A(x - A(x)))) = x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^11 +...
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 +...
...
The series reversion of A(x) is the g.f. of A228862, which begins:
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 +...
PROG
(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)}
for(n=1, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Sep 05 2013
STATUS
approved