A213099 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^7)^3.

1, 1, 3, 18, 112, 909, 7833, 74603, 740541, 7656219, 81187518, 878435208, 9647220024, 107137240686, 1199914011387, 13521738420240, 153051832116378, 1737562815056865, 19762347822563532, 224970273310192579, 2561375647064514444, 29149168085832027732

Offset: 0

Author

Paul D. Hanna, Jun 05 2012

Keywords

• sign

Comments

Compare definition of g.f. to:

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

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

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

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

(5) F(x) = 1 + x/F(-x*F(x)^9)^5 when F(x) = 1 + x*F(x)^5 (A002294).

The first negative term is a(121). - Georg Fischer, Feb 16 2019

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 18*x^3 + 112*x^4 + 909*x^5 + 7833*x^6 +...
Related expansions:
A(x)^7 = 1 + 7*x + 42*x^2 + 287*x^3 + 2079*x^4 + 16611*x^5 + 142702*x^6 +...
A(-x*A(x)^7)^3 = 1 - 3*x - 9*x^2 - 31*x^3 - 318*x^4 - 2586*x^5 - 25969*x^6 -...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000108, A001764, A002293, A002294, A213091, A213092, A213093, A213094, A213095, A213096, A213098, A213100, A213101, A213102, A213103, A213104, A213105.

Programs

Mathematica

m = 22; A[] = 1; Do[A[x] = 1 + x/A[-x A[x]^7]^3 + O[x]^m, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Nov 06 2019 *)

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^7,x,x+x*O(x^n))) );polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))