OFFSET
1,2
COMMENTS
Compare to: G(x) = x*exp( Sum_{n>=1} G(x^n)/n ), which is the g.f. of A000081, the number of rooted trees with n nodes.
FORMULA
Limit a(n) / 2^(n*(n-1)/2) = 2.4760521181770989525583758338042055853633514575492...
EXAMPLE
G.f.: A(x) = x + 2*x^2 + 12*x^3 + 120*x^4 + 2208*x^5 + 75840*x^6 + 5026048*x^7 + ...
where
A(x) = x*exp(A(2*x) + A(4*x^2)/2 + A(8*x^3)/3 + A(16*x^4)/4 + A(32*x^5)/5 + A(64*x^6)/6 + A(128*x^7)/7 + A(256*x^8)/8 + A(512*x^9)/9 + A(1024*x^10)/10 + ...).
PROG
(PARI) {a(n)=local(A=x); for(i=1, n, A=x*exp(sum(k=1, n, subst(A, x, 2^k*x^k +x*O(x^n))/k))); polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 03 2013
STATUS
approved