A213098 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^6)^2.

1, 1, 2, 11, 56, 401, 2960, 23909, 199324, 1704937, 14871560, 131002444, 1162055526, 10330588405, 91813523884, 814261196562, 7195489202430, 63317110066321, 554812081610114, 4845145547265182, 42242647963009666, 368598374017590156, 3228911122031762918

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).

The first negative term is a(67). - Georg Fischer, Feb 16 2019

Links

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 11*x^3 + 56*x^4 + 401*x^5 + 2960*x^6 +...
Related expansions:
A(x)^6 = 1 + 6*x + 27*x^2 + 146*x^3 + 861*x^4 + 5772*x^5 + 42206*x^6 +...
A(-x*A(x)^6)^2 = 1 - 2*x - 7*x^2 - 20*x^3 - 172*x^4 - 1202*x^5 - 9766*x^6 -...

Mathematica

m = 23; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^6]^2 + 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^2, x, -x*subst(A^6, x, x+x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

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

Sequence in context: A037554 A106804 A361219 * A041129 A332524 A037490

Adjacent sequences: A213095 A213096 A213097 * A213099 A213100 A213101

Keyword

sign

Author

Paul D. Hanna, Jun 05 2012

Status

approved