OFFSET
0,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..330
FORMULA
a(n) ~ c * n^n / (exp(n) * (log(2))^n), where c = 1.16670181891916121...
MATHEMATICA
nmax = 21; sol = {a[0] -> 1};
Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[2 A[x] - (1 + x + A[x A[x]]) + O[x]^(n+1), x] == 0 /. sol; sol = sol ~Join~ Solve[eq][[1]], {n, 1, nmax}];
sol /. Rule -> Set;
a /@ Range[0, nmax] (* Jean-François Alcover, Nov 01 2019 *)
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A = 1+x + subst(A, x, x*A +x*O(x^n)) - A); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 11 2014
EXTENSIONS
STATUS
approved