OFFSET
0,4
COMMENTS
The g.f. of A141200 satisfies: B(x) = x + B(B(x)^2).
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..512
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 2.20085985704067535258..., c = 4.25914484723... if n is even and c = 4.40480643955... if n is odd. - Vaclav Kotesovec, Dec 02 2014
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 10*x^6 + 21*x^7 +...
If B(x) = g.f. of A141200, with B(x/A(x)) = x and B(x) = x + B(B(x)^2), then
B(x) = x + x^2 + 2*x^3 + 6*x^4 + 20*x^5 + 72*x^6 + 272*x^7 +... where
x/A(x) = x - (x^2 + x^4 + 2*x^6 + 6*x^8 + 20*x^10 + 72*x^12 + 272*x^14 +...)
A(B(x)) = B(x)/x = 1 + x + 2*x^2 + 6*x^3 + 20*x^4 + 72*x^5 + 272*x^6 +...
PROG
(PARI) {a(n)=local(A=1+x+x^2*O(x^n)); for(i=0, #binary(n)+1, A=x/(x-subst(serreverse(x/A), x, x^2+x^2*O(x^n)))) ; polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 11 2010
STATUS
approved