OFFSET
0,3
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 19*x^3 + 299*x^4 + 6241*x^5 + 160020*x^6 + 4858616*x^7 + 171069361*x^8 + 6885389368*x^9 + 313162056098*x^10 + ...
such that g.f. A = A(x) satisfies:
A(x) = 1 + x*(1 + (A - 1/A) + (A^2 - 1/A^2)^2 + (A^3 - 1/A^3)^3 + (A^4 - 1/A^4)^4 + (A^5 - 1/A^5)^5 + ...).
RELATED SERIES.
x/Series_Reversion(A(x) - 1) = 1 + 2*x + 15*x^2 + 201*x^3 + 3807*x^4 + 93103*x^5 + 2788528*x^6 + 98816388*x^7 + 4043274742*x^8 + 187583369889*x^9 + 9729671519992*x^10 + ...
PROG
(PARI) {a(n) = my(A=1); for(i=1, n, A = 1 + x*sum(m=0, n, (A^m - 1/A^m +x*O(x^n))^m )); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 15 2018
STATUS
approved