OFFSET
1,5
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..100
FORMULA
G.f. A(x) satisfies: A(A(x)) = x.
EXAMPLE
G.f.: A(x) = -x + x^2 - x^3 - x^4 + 5*x^5 - 8*x^6 - x^7 + 30*x^8 - 54*x^9 - 5*x^10 + 179*x^11 - 178*x^12 - 608*x^13 + 1518*x^14 + 2611*x^15 - 18198*x^16 + ...
such that
1 = 1 + (x + A(x)) + (x + A(x)^2)*(x^2 + A(x)) + (x + A(x)^3)*(x^2 + A(x)^2)*(x^3 + A(x)) + (x + A(x)^4)*(x^2 + A(x)^3)*(x^3 + A(x)^2)*(x^4 + A(x)) + (x + A(x)^5)*(x^2 + A(x)^4)*(x^3 + A(x)^3)*(x^4 + A(x)^2)*(x^5 + A(x)) + ...
also, A(A(x)) = x.
PROG
(PARI) {a(n) = my(A=[-1]); for(i=1, n, A = concat(A, 0); A[#A] = -Vec( sum(n=0, #A, prod(k=1, n, x^(n+1-k) + (x*Ser(A))^k ) ) )[#A+1] ); A[n]}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jun 23 2018
STATUS
approved