%I
%S 1,1,2,6,22,90,394,1806,8558,41586,206098,1037718,5293446,
%T 27297738,142078746,745387038,3937603038,20927156706,
%U 111818026018,600318853926,3236724317174,17518619320890,95149655201962
%N Expansion of (1 + x + sqrt(1  6*x + x^2))/2 in powers of x.
%C Series reversion of x(Sum_{k>=0} a(k)x^k) is x(Sum_{k>=0} A003168(k)x^k).
%C G.f. A(x) = Sum_{k>=0} a(k)x^k satisfies 0 = 2*x  (x + 1)*A(x) + A(x)^2.
%H Foissy, Loic, <a href="https://doi.org/10.1007/s1080101203580">Algebraic structures on double and plane posets</a>, J. Algebr. Comb. 37, No. 1, 3966 (2013).
%F G.f.: (1 + x + sqrt(1  6*x + x^2))/2. (= 1/g.f. A001003)
%F Dfinite: n*a(n) + 3*(2*n + 3)*a(n1) + (n3)*a(n2) = 0.  _R. J. Mathar_, Jul 23 2017
%t ReciprocalSeries[ser_, n_] := CoefficientList[ Series[1/ser, {x, 0, n}], x];
%t LittleSchroeder := (1 + x  Sqrt[1  6 x + x^2])/(4 x); (* A001003 *)
%t ReciprocalSeries[LittleSchroeder, 22] (* _Peter Luschny_, Jan 10 2019 *)
%o (PARI) a(n)=polcoeff((1+x+sqrt(16*x+x^2+x*O(x^n)))/2,n)
%Y A minor variation of A006318. a(n)=A006318(n1), n>0. a(n)=A085403(n), n>1.
%Y Cf. A001003.
%K sign
%O 0,3
%A _Michael Somos_, Jul 20 2003
