A213102 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^9)^4.

1, 1, 4, 30, 240, 2433, 26388, 315726, 3958452, 51863952, 698988716, 9637772716, 135161761860, 1920878419569, 27583547221596, 399310273694328, 5817100622299116, 85152975761167179, 1251046169511714720, 18428780031111768466, 271964652432415737596

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(142). - Georg Fischer, Feb 16 2019

Examples

			G.f.: A(x) = 1 + x + 4*x^2 + 30*x^3 + 240*x^4 + 2433*x^5 + 26388*x^6 +...
Related expansions:
A(x)^9 = 1 + 9*x + 72*x^2 + 642*x^3 + 6030*x^4 + 61551*x^5 + 670344*x^6 +...
A(-x*A(x)^9)^4 = 1 - 4*x - 14*x^2 - 64*x^3 - 797*x^4 - 8188*x^5 - 104090*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, A213099, A213100, A213101, A213103, A213104, A213105.

Programs

Mathematica

m = 21; A[] = 1; Do[A[x] = 1 + x/A[-x A[x]^9]^4 + 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^4,x,-x*subst(A^9,x,x+x*O(x^n))) );polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))