OFFSET
0,3
COMMENTS
Terms seem to be doubly-exponential: log(a(n+1))/log(a(n)) ~ c where c = 1.44...
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 53*x^4 + 1305*x^5 + 177559*x^6 +...
The logarithm of g.f. A(x) begins:
log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 183*x^4/4 + 6236*x^5/5 + 1057176*x^6/6 + 1733913028*x^7/7 + 74017764628367*x^8/8 +...+ A180721(n)*x^n/n +...
which also equals the series:
log(A(x)) = A(x)*x + A(3*x)^2*x^2/2 + A(16*x)^3*x^3/3 + A(183*x)^4*x^4/4 + A(6236*x)^5*x^5/5 + A(1057176*x)^6*x^6/6 + A(1733913028*x)^7*x^7/7 +...+ A(A180721(n)*x)^n*x^n/n + ...
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n), L); for(i=1, n, L=Vec(deriv(log(A))); A=exp(sum(m=1, #L, subst(A, x, L[m]*x)^m*x^m/m)+x*O(x^n))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 19 2010
STATUS
approved