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)^7))/2 starting at G_0(x) = 1+2*x.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 16*x^2 + 144*x^3 + 1280*x^4 + 12416*x^5 + 156288*x^6 +...
A(x)^4 = 1 + 8*x + 88*x^2 + 992*x^3 + 10896*x^4 + 121600*x^5 + 1492480*x^6 +...
A(x)^7 = 1 + 14*x + 196*x^2 + 2632*x^3 + 33712*x^4 + 424032*x^5 + 5484864*x^6 +...
PROG
(PARI) {a(n)=local(A=1+2*x); for(i=0, n, A=(A+1/subst(A, x, -x*A^7+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