OFFSET
0,3
COMMENTS
Compare to g.f. exp( Sum_{m>=1} (1 + x)^m * x^m/m ) of the Fibonacci sequence.
Conjecture: a(n)^(1/n^2) tends to 2^(1/4). - Vaclav Kotesovec, Oct 17 2020
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..150
FORMULA
G.f.: A(x) = exp(F(x)) where F(x) is the l.g.f. of A156101.
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 25*x^4 + 113*x^5 + 741*x^6 +...
log(A(x)) = (1 + 2*x)*x + (1 + 2^2*x)^2*x^2/2 + (1 + 2^3*x)^3*x^3/3 +...
log(A(x)) = x + 5*x^2/2 + 13*x^3/3 + 65*x^4/4 + 401*x^5/5 + 3521*x^6/6 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (1+2^m*x)^m*x^m/m)+x*O(x^n)), n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 04 2009
STATUS
approved