OFFSET
1,2
COMMENTS
A generator is a leaf or a node with just one child.
LINKS
FORMULA
E.g.f. satisfies: (2-x)*A(x) = x - 1 - log(1-A(x)).
a(n) ~ c * n^(n-1) / (exp(n) * r^n), where r = 0.20846306198165450115960050053484328028... and c = 0.3060161306524907981116283162103879... - Vaclav Kotesovec, Mar 28 2014
MATHEMATICA
nmax=20; c[0]=0; A[x_]:=Sum[c[k]*x^k/k!, {k, 0, nmax}]; Array[c, nmax]/.Solve[Rest[CoefficientList[Series[x-1-Log[1-A[x]]-(2-x)*A[x], {x, 0, nmax}], x]]==0][[1]] (* Vaclav Kotesovec, Mar 28 2014 *)
PROG
(PARI) {a(n)=local(A=x+O(x^n)); for(i=0, n, A=intformal((1-A^2)/(1-x-2*A+x*A)+O(x^n))); n!*polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Mar 28 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jun 07 2005
STATUS
approved
