OFFSET
2,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 2..301
FORMULA
G.f. A(x) = Sum_{n>=2} a(n)*x^n satisfies the following formulas.
(1) A(x - A(x)) = x^2 - x^3.
(2) A(x) = B(x)^2 - B(x)^3 where B(x) = x + A(B(x)) is the g.f. of A190761 and B(x - A(x)) = x.
EXAMPLE
G.f.: A(x) = x^2 + x^3 + 4*x^4 + 22*x^5 + 144*x^6 + 1064*x^7 + 8623*x^8 + 75267*x^9 + 698898*x^10 + 6843478*x^11 + 70209485*x^12 + ...
where A(x - A(x)) = x^2 - x^3.
RELATED SERIES.
Let B(x) be the g.f. of A190761, then A(x) = B(x)^2 - B(x)^3 where
B(x) = x + x^2 + 3*x^3 + 14*x^4 + 84*x^5 + 592*x^6 + 4670*x^7 + ...
Also,
A(B(x)) = x^2 + 3*x^3 + 14*x^4 + 84*x^5 + 592*x^6 + 4670*x^7 + ...
PROG
(PARI) {a(n) = my(A=x^2, B=x);
for(i=1, n, A = B^2 - B^3 +x*O(x^n); B = x + subst(A, x, B) ); polcoeff(A, n)}
for(n=2, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 30 2023
STATUS
approved