A213098 - OEIS

%I #14 Nov 06 2019 04:21:55

%S 1,1,2,11,56,401,2960,23909,199324,1704937,14871560,131002444,

%T 1162055526,10330588405,91813523884,814261196562,7195489202430,

%U 63317110066321,554812081610114,4845145547265182,42242647963009666,368598374017590156,3228911122031762918

%N G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^6)^2.

%C Compare definition of g.f. to:

%C (1) B(x) = 1 + x/B(-x*B(x)) when B(x) = 1/(1-x).

%C (2) C(x) = 1 + x/C(-x*C(x)^3)^2 when C(x) = 1 + x*C(x)^2 (A000108).

%C (3) D(x) = 1 + x/D(-x*D(x)^5)^3 when D(x) = 1 + x*D(x)^3 (A001764).

%C (4) E(x) = 1 + x/E(-x*E(x)^7)^4 when E(x) = 1 + x*E(x)^4 (A002293).

%C The first negative term is a(67). - _Georg Fischer_, Feb 16 2019

%H Paul D. Hanna, <a href="/A213098/b213098.txt">Table of n, a(n) for n = 0..300</a>

%e G.f.: A(x) = 1 + x + 2*x^2 + 11*x^3 + 56*x^4 + 401*x^5 + 2960*x^6 +...

%e Related expansions:

%e A(x)^6 = 1 + 6*x + 27*x^2 + 146*x^3 + 861*x^4 + 5772*x^5 + 42206*x^6 +...

%e A(-x*A(x)^6)^2 = 1 - 2*x - 7*x^2 - 20*x^3 - 172*x^4 - 1202*x^5 - 9766*x^6 -...

%t m = 23; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^6]^2 + O[x]^m, {m}];

%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Nov 06 2019 *)

%o (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+x/subst(A^2,x,-x*subst(A^6,x,x+x*O(x^n))) );polcoeff(A,n)}

%o for(n=0,30,print1(a(n),", "))

%Y Cf. A000108, A001764, A002293, A213091, A213092, A213093, A213094, A213095, A213096, A213099, A213100, A213101, A213102, A213103, A213104, A213105.

%K sign

%O 0,3

%A _Paul D. Hanna_, Jun 05 2012