OFFSET
0,2
COMMENTS
FORMULA
The g.f. of this sequence is the limit of the recurrence:
(*) G_{n+1}(x) = (G_n(x) + 1/G_n(-x*G_n(x)^5))/2 starting at G_0(x) = 1+2*x.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 12*x^2 + 84*x^3 + 616*x^4 + 4832*x^5 + 42112*x^6 +...
A(x)^3 = 1 + 6*x + 48*x^2 + 404*x^3 + 3432*x^4 + 29808*x^5 + 271056*x^6 +...
A(x)^5 = 1 + 10*x + 100*x^2 + 980*x^3 + 9400*x^4 + 89632*x^5 + 866080*x^6 +...
PROG
(PARI) {a(n)=local(A=1+2*x); for(i=0, n, A=(A+1/subst(A, x, -x*A^5+x*O(x^n)))/2); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 29 2012
STATUS
approved