0,3

G.f.: A(x) = 1 + x*B(x)^3; B(x) = 1 + 2*x*C(x)^3; C(x) = 1 + 3*x*D(x)^3; D(x) = 1 + 4*x*E(x)^3; E(x) = 1 + 5*x*F(x)^3; F(x) = 1 + 6*x*G(x)^3; ...

where the respective sequences begin:

A=[1,1,6,66,1034,20790,507600,14546196,478095264,...];

B=[1,2,18,270,5454,135936,3992544,134386344,5088220200,...];

C=[1,3,36,684,16932,504540,17367840,673851600,28994802120,...];

D=[1,4,60,1380,40460,1404000,55499040,2443032360,118003755960,...];

E=[1,5,90,2430,82350,3262770,145741680,7183818180,385393611960,...];

F=[1,6,126,3906,150234,6693120,333506880,18208871856,1075094932464,...];

G=[1,7,168,5880,253064,12523896,688855104,41282607744,2661610538160,..];

H=[1,8,216,8424,401112,21833280,1314118080,85783244400,5998813428240,..];

(PARI) {a(n)=local(A=1+(n+1)*x); for(k=0, n, A=1+(n-k+1)*x*A^3 +x*O(x^n)); polcoeff(A, n)}

Cf. A128318.

Sequence in context: A124862 A130977 A133306 this_sequence A008548 A090358 A112942

Adjacent sequences: A128316 A128317 A128318 this_sequence A128320 A128321 A128322

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Mar 07 2007