OFFSET
0,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..333
FORMULA
G.f. satisfies: A(x)^2 = A(x*A(x)) + x*A(x).
a(n) ~ (n-1)! / (4 * (log(2))^(n+1)). - Vaclav Kotesovec, Feb 12 2015
O.g.f.: A(x) = x/( series reversion x*B(x) ), where B(x) = 1 + x + 2*x^2 + 6*x^3 + 25*x^4 + 137*x^5 + ... is the o.g.f. of A084784. - Peter Bala, Jun 23 2015
MATHEMATICA
nmax = 19; sol = {a[0] -> 1};
Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[A[x]^2 - (A[x A[x]] + 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 02 2019 *)
PROG
(PARI) {a(n)=local(A, m); if(n<1, n==0, m=1; A=1+x; for(i=1, n, A=(subst(A, x, x*A+x*O(x^n)) + x*A)/A); polcoeff(A, n))}
for(n=0, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Feb 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul D. Hanna, Oct 16 2003
STATUS
approved