cp's OEIS Frontend

A213096 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^6)^3.

%I A213096 #12 Nov 05 2019 12:01:57
%S A213096 1,1,3,15,82,549,3957,31423,262905,2309655,20954053,195219912,
%T A213096 1855139472,17913275558,175183126884,1731034436637,17250012004590,
%U A213096 173095950538881,1746875271992760,17712083908168204,180276161806773003,1840572737915529150,18838475627464850819
%N A213096 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^6)^3.
%C A213096 Compare definition of g.f. to:
%C A213096 (1) B(x) = 1 + x/B(-x*B(x)) when B(x) = 1/(1-x).
%C A213096 (2) C(x) = 1 + x/C(-x*C(x)^3)^2 when C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).
%C A213096 (3) D(x) = 1 + x/D(-x*D(x)^5)^3 when D(x) = 1 + x*D(x)^3 is the g.f. of the ternary tree numbers (A001764).
%C A213096 The first negative term is a(193). - _Georg Fischer_, Feb 16 2019
%H A213096 Paul D. Hanna, <a href="/A213096/b213096.txt">Table of n, a(n) for n = 0..300</a>
%e A213096 G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 82*x^4 + 549*x^5 + 3957*x^6 +...
%e A213096 Related expansions:
%e A213096 A(x)^6 = 1 + 6*x + 33*x^2 + 200*x^3 + 1272*x^4 + 8730*x^5 + 63628*x^6 +...
%e A213096 A(-x*A(x)^6)^3 = 1 - 3*x - 6*x^2 - 19*x^3 - 156*x^4 - 1065*x^5 - 9165*x^6 -...
%t A213096 m = 22; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^6 + O[x]^m]^3 // Normal, {m}];
%t A213096 CoefficientList[A[x], x] (* _Jean-François Alcover_, Nov 05 2019 *)
%o A213096 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x/subst(A^3,x,-x*subst(A^6,x,x+x*O(x^n))) );polcoeff(A,n)}
%o A213096 for(n=0,30,print1(a(n),", "))
%Y A213096 Cf. A000108, A001764, A213091, A213092, A213093, A213094, A213095.
%K A213096 sign
%O A213096 0,3
%A A213096 _Paul D. Hanna_, Jun 05 2012