A213095 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^5)^2.

1, 1, 2, 9, 40, 242, 1528, 10664, 76956, 575245, 4395910, 34131621, 268146598, 2122399923, 16884293154, 134689290877, 1075641369024, 8588548510081, 68496446989330, 545303352881863, 4331918361300882, 34337864000400360, 271657823631727330, 2146133623039711577

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 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(85). - Georg Fischer, Feb 16 2019

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 26*x^4 + 123*x^5 + 622*x^6 + 3490*x^7 +...
Related expansions:
A(x)^5 = 1 + 5*x + 20*x^2 + 95*x^3 + 485*x^4 + 2801*x^5 + 17560*x^6 +...
A(-x*A(x)^5)^2 = 1 - 2*x - 5*x^2 - 12*x^3 - 93*x^4 - 550*x^5 - 3981*x^6 -...
		

Links

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

Crossrefs

Cf. A000108, A001764, A213091, A213092, A213093, A213094, A213096.

Programs

Mathematica

m = 23; A[] = 1; Do[A[x] = 1 + x/A[-x A[x]^5 + O[x]^m]^2 // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Nov 05 2019 *)

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^5,x,x+x*O(x^n))) );polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))