%I #5 Oct 29 2019 16:18:10
%S 1,1,5,39,345,3512,38431,451620,5587237,72275004,968509140,
%T 13361356169,188704259571,2716467168169,39716842554828,
%U 588125693790055,8800638181341593,132838773216409675,2019626662710709088,30891440565153652705,474899505740289874276
%N G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^10)^4).
%C Compare g.f. to:
%C (1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
%C (2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
%C (3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
%C (4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).
%e G.f.: A(x) = 1 + x + 5*x^2 + 39*x^3 + 345*x^4 + 3512*x^5 + 38431*x^6 +...
%e Related expansions:
%e A(x)^10 = 1 + 10*x + 95*x^2 + 960*x^3 + 10095*x^4 + 111212*x^5 +...
%e 1/A(-x*A(x)^10)^4 = 1 + 4*x + 30*x^2 + 256*x^3 + 2605*x^4 + 28484*x^5 +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A^4, x, -x*subst(A^10, x, x+x*O(x^n)))) ); polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A213225, A213226, A213227, A213228, A213229, A213230, A213231, A213232.
%Y Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.
%Y Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.
%Y Cf. A213108, A213109, A213110, A213111, A213112, A213113.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 06 2012