A213104 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^10)^5.

1, 1, 5, 40, 360, 3820, 43651, 543240, 7146185, 98885725, 1420274645, 21037156031, 319127602075, 4935547265370, 77525696636995, 1233356748777015, 19829269320322346, 321631227310756885, 5255920261950786655, 86436636022328320125, 1429253483704685851315

Offset

0,3

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).

(6) G(x) = 1 + x/G(-x*G(x)^11)^6 when G(x) = 1 + x*G(x)^6 (A002295).

The first negative term is a(306). - Georg Fischer, Feb 16 2019

Links

Paul D. Hanna, Table of n, a(n) for n = 0..400

Example

G.f.: A(x) = 1 + x + 5*x^2 + 40*x^3 + 360*x^4 + 3820*x^5 + 43651*x^6 +...
Related expansions:
A(x)^10 = 1 + 10*x + 95*x^2 + 970*x^3 + 10335*x^4 + 116452*x^5 +...
A(-x*A(x)^10)^5 = 1 - 5*x - 15*x^2 - 85*x^3 - 995*x^4 - 10776*x^5 -...

Mathematica

m = 21; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^10]^5 + O[x]^m, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Nov 06 2019 *)

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x/subst(A^5, x, -x*subst(A^10, x, x+x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A000108, A001764, A002293, A002294, A002295, A213091, A213092, A213093, A213094, A213095, A213096, A213098, A213099, A213100, A213101, A213102, A213103, A213105.

Sequence in context: A137973 A371520 A052788 * A219560 A349362 A359984

Adjacent sequences: A213101 A213102 A213103 * A213105 A213106 A213107

Keyword

sign

Author

Paul D. Hanna, Jun 05 2012

Status

approved