OFFSET
1,2
COMMENTS
A generator is a leaf or a node with just one child.
In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root.
LINKS
FORMULA
E.g.f. satisfies: 2*A(x) = x - 1 + exp(A(x)) + Integral A(x) dx. - corrected by Vaclav Kotesovec and Paul D. Hanna, Mar 29 2014
From Paul D. Hanna, Mar 29 2014: (Start)
E.g.f. satisfies: A(x) = A'(x)*(2 - exp(A(x))) - 1.
E.g.f. satisfies: A'(x) = (1 + A(x))/(2 - exp(A(x)).
(End)
a(n) ~ c * n^(n-1) / (exp(n) * r^n), where r = 0.3160173586544089316502903103262192204293322854083... and c = 0.51723490785798357350192800634304... - Vaclav Kotesovec, Mar 29 2014
PROG
(PARI) {a(n)=local(A=x); for(i=1, n, A=intformal((1+A)/(2-exp(A+x*O(x^n)))) ); n!*polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Mar 29 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jun 07 2005
STATUS
approved