A213096 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^6)^3.

1, 1, 3, 15, 82, 549, 3957, 31423, 262905, 2309655, 20954053, 195219912, 1855139472, 17913275558, 175183126884, 1731034436637, 17250012004590, 173095950538881, 1746875271992760, 17712083908168204, 180276161806773003, 1840572737915529150, 18838475627464850819

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 is the g.f. of the Catalan numbers (A000108).

(3) D(x) = 1 + x/D(-x*D(x)^5)^3 when D(x) = 1 + x*D(x)^3 is the g.f. of the ternary tree numbers (A001764).

The first negative term is a(193). - 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 + 15*x^3 + 82*x^4 + 549*x^5 + 3957*x^6 +...
Related expansions:
A(x)^6 = 1 + 6*x + 33*x^2 + 200*x^3 + 1272*x^4 + 8730*x^5 + 63628*x^6 +...
A(-x*A(x)^6)^3 = 1 - 3*x - 6*x^2 - 19*x^3 - 156*x^4 - 1065*x^5 - 9165*x^6 -...

Mathematica

m = 22; A[_] = 1; Do[A[x_] = 1 + x/A[-x A[x]^6 + O[x]^m]^3 // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Nov 05 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^6, x, x+x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A000108, A001764, A213091, A213092, A213093, A213094, A213095.

Sequence in context: A371616 A203507 A192662 * A052451 A026019 A354660

Adjacent sequences: A213093 A213094 A213095 * A213097 A213098 A213099

Keyword

sign

Author

Paul D. Hanna, Jun 05 2012

Status

approved