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

0,3

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).

Links

Table of n, a(n) for n=0..21.

Example

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 +...

Prog

(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), ", "))

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.

Sequence in context: A213608 A369325 A324169 * A051820 A362206 A364759

Adjacent sequences: A213228 A213229 A213230 * A213232 A213233 A213234

Keyword

nonn

Author

Paul D. Hanna, Jun 06 2012

Status

approved