A213228 G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^6)^2).

1, 1, 3, 14, 73, 440, 2862, 19991, 146939, 1125413, 8896018, 72067978, 595097838, 4987609871, 42290465703, 361845473658, 3117830204185, 27009650432888, 234932107635587, 2049479335366836, 17915253987741538, 156799716352350344, 1373180896765862962

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..22.

Example

 G.f.: A(x) = 1 + x + 3*x^2 + 14*x^3 + 73*x^4 + 440*x^5 + 2862*x^6 +...
Related expansions:
A(x)^6 = 1 + 6*x + 33*x^2 + 194*x^3 + 1188*x^4 + 7656*x^5 + 51583*x^6 +...
1/A(-x*A(x)^6)^2 = 1 + 2*x + 9*x^2 + 44*x^3 + 268*x^4 + 1750*x^5 + 12422*x^6 +...

Prog

 (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^6, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A213225, A213226, A213227, A213229, A213230, 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.

Sequence in context: A295104 A080238 A307443 * A306455 A277939 A210346

Adjacent sequences: A213225 A213226 A213227 * A213229 A213230 A213231

Keyword

nonn

Author

Paul D. Hanna, Jun 06 2012

Status

approved