A213231 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^8)^3).

1, 1, 4, 25, 176, 1431, 12526, 117850, 1167446, 12080563, 129326575, 1422908670, 15999766613, 183070661566, 2124252427416, 24929036429880, 295250330398281, 3523043486823439, 42294807342916249, 510274778010082846, 6181011777164665559, 75112032752942278141

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 + 4*x^2 + 25*x^3 + 176*x^4 + 1431*x^5 + 12526*x^6 +...
Related expansions:
A(x)^8 = 1 + 8*x + 60*x^2 + 480*x^3 + 3998*x^4 + 34968*x^5 + 318888*x^6 +...
1/A(-x*A(x)^8)^3 = 1 + 3*x + 18*x^2 + 121*x^3 + 987*x^4 + 8646*x^5 + 82244*x^6 +...
		

Crossrefs

Cf. A213225, A213226, A213227, A213228, A213229, A213230, 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^3, x, -x*subst(A^8, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))