A213230 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^8)^2).

1, 1, 3, 18, 115, 902, 7722, 70784, 678251, 6670586, 66851992, 677328214, 6903177354, 70490174298, 718856047396, 7304677030708, 73837797474235, 741722190452840, 7402780597473820, 73459355234486763, 726095774886910232, 7170907377415662763, 71063833561266044578

Offset: 0

Author

Paul D. Hanna, Jun 06 2012

Keywords

• nonn

Comments

Compare g.f. to:

(1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).

(2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).

(3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).

(4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 18*x^3 + 115*x^4 + 902*x^5 + 7722*x^6 +...
Related expansions:
A(x)^8 = 1 + 8*x + 52*x^2 + 368*x^3 + 2754*x^4 + 22112*x^5 + 189344*x^6 +...
1/A(-x*A(x)^8)^2 = 1 + 2*x + 13*x^2 + 78*x^3 + 634*x^4 + 5488*x^5 + 50969*x^6 +...
		

Crossrefs

Cf. A213225, A213226, A213227, A213228, A213229, A213231, A213232, A213233.

Cf. A213091, A213092, A213093, A213094, A213095, A213096, A213098.

Cf. A213099, A213100, A213101, A213102, A213103, A213104, A213105.

Cf. A213108, A213109, A213110, A213111, A213112, A213113.

Programs

PARI

{a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A^2, x, -x*subst(A^8, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))