OFFSET
1,4
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..520
EXAMPLE
G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 2*x^5 + 3*x^6 + 5*x^7 + 9*x^8 + 18*x^9 + 38*x^10 + 79*x^11 + 162*x^12 + 330*x^13 + 661*x^14 + 1323*x^15 + 2661*x^16 +...
such that A(x*A(-x)) = x^3 - x^2.
RELATED SERIES.
Let B(x) be the series reversion of g.f. A(x), so that A(B(x)) = x, then
B(x) = x - x^2 + x^3 - 2*x^4 + 6*x^5 - 17*x^6 + 45*x^7 - 123*x^8 + 356*x^9 - 1061*x^10 + 3193*x^11 - 9691*x^12 + 29741*x^13 - 92228*x^14 +...+ (-1)^(n-1)*A268655(n)*x^n +...
where B(x^3 - x^2) = x*A(-x),
also, B(B(x^3-x^2)/x) = -x.
PROG
(PARI) {a(n) = my(A=[1, 1], F); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A] = Vec(subst(F, x, -x*F))[#A]); A[n]}
for(n=1, 50, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 15 2016
STATUS
approved