OFFSET
0,3
COMMENTS
Limit n->infinity (a(n)/n!)^(1/n) = 1.1453530527... - Vaclav Kotesovec, Feb 24 2014
Compare to: G(x) = exp(Integral G(x) dx) when G(x) = 1/(1-x).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..200
FORMULA
E.g.f. A(x) satisfies: log(A(x)) = x*A'(x)/A(x) - x^2*A(x).
EXAMPLE
E.g.f. A(x) = 1 + x + 3*x^2/2! + 10*x^3/3! + 49*x^4/4! + 281*x^5/5! +...
log(A(x)) = x + x^2 + x^3/2! + 3*x^4/3! + 10*x^5/4! + 49*x^6/5! +...
A'(x)/A(x) = 1 + 2*x + 3*x^2/2! + 12*x^3/3! + 50*x^4/4! + 294*x^5/5! +...
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=exp(x+x*intformal(A))); n!*polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 06 2008
STATUS
approved