OFFSET
1,4
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..150
FORMULA
G.f. A(x) satisfies: A(A(x)) = x.
EXAMPLE
G.f.: A(x) = -x + x^2 - x^3 - 2*x^4 + 8*x^5 + 56*x^6 - 281*x^7 - 3061*x^8 + 18612*x^9 + 271129*x^10 - 1925781*x^11 - 34967550*x^12 + 284063311*x^13 + 6174304311*x^14 - 56535769915*x^15 - 1431894779510*x^16 + ...
such that
1 = 1 + (x + A(x)) + (x + 2*A(x))*(2*x + A(x)) + (x + 3*A(x))*(2*x + 2*A(x))*(3*x + A(x)) + (x + 4*A(x))*(2*x + 3*A(x))*(3*x + 2*A(x))*(4*x + A(x)) + (x + 5*A(x))*(2*x + 4*A(x))*(3*x + 3*A(x))*(4*x + 2*A(x))*(5*x + 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, (n+1-k)*x + (k)*x*Ser(A) ) ) )[#A+1] ); A[n]}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jun 23 2018
STATUS
approved