A213100 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^9)^3.

1, 1, 3, 24, 181, 1893, 20601, 245176, 3018669, 38198478, 493218343, 6441378129, 84807054552, 1120545910725, 14820493111536, 195812569428897, 2580287366558579, 33878771120862777, 443012040333754728, 5770422757461475027, 74931929672784252306

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).

The first negative term is a(68). - 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 + 3*x^2 + 24*x^3 + 181*x^4 + 1893*x^5 + 20601*x^6 +...
Related expansions:
A(x)^9 = 1 + 9*x + 63*x^2 + 516*x^3 + 4563*x^4 + 45207*x^5 + 486579*x^6 +...
A(-x*A(x)^9)^3 = 1 - 3*x - 15*x^2 - 64*x^3 - 798*x^4 - 8277*x^5 - 99411*x^6 -...

Mathematica

m = 21; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^9]^3 + 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^3, x, -x*subst(A^9, x, x+x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A000108, A001764, A002293, A002294, A213091, A213092, A213093, A213094, A213095, A213096, A213098, A213099, A213101, A213102, A213103, A213104, A213105.

Sequence in context: A181967 A144087 A110347 * A027324 A122741 A136325

Adjacent sequences: A213097 A213098 A213099 * A213101 A213102 A213103

Keyword

sign

Author

Paul D. Hanna, Jun 05 2012

Status

approved