A138916 G.f. A(x) satisfies: 7*A(x) = A(A(A(A(A(A(x)))))) + 6*x + x^2 with A(0)=0.

1, 1, 30, 2385, 273560, 39078970, 6512700536, 1222156339336, 252751878117712, 56798072762849412, 13733835430565197700, 3548014267149570778764, 974073193845291808779496, 283008950620416071533339000

Offset

1,3

Comments

A(A(A(A(A(A(x)))))) is the 6th self-composition of the g.f. A(x).

Links

Table of n, a(n) for n=1..14.

Example

G.f.: A(x) = x + x^2 + 30*x^3 + 2385*x^4 + 273560*x^5 +...
A(A(x)) = x + 2*x^2 + 62*x^3 + 4921*x^4 + 564280*x^5 +...
A(A(A(x))) = x + 3*x^2 + 96*x^3 + 7614*x^4 + 872950*x^5 +...
A(A(A(A(x)))) = x + 4*x^2 + 132*x^3 + 10470*x^4 + 1200384*x^5 +...
A(A(A(A(A(x))))) = x + 5*x^2 + 170*x^3 + 13495*x^4 + 1547420*x^5 +...
A(A(A(A(A(A(x)))))) = x + 6*x^2 + 210*x^3 + 16695*x^4 + 1914920*x^5 +...
so that 7*A(x) = A(A(A(A(A(A(x)))))) + 6*x + x^2.

Prog

(PARI) {a(n)=local(A=x+x^2, G); if(n<1, 0, for(i=3, n+1, G=x; for(j=1, 6, G=subst(A, x, G+x*O(x^i))); A=A+polcoeff(G, i)*x^i); polcoeff(A, n))}

Crossrefs

Cf. A138739, A138913, A138914, A138915.

Sequence in context: A061162 A230272 A230612 * A266041 A091544 A230728

Adjacent sequences: A138913 A138914 A138915 * A138917 A138918 A138919

Keyword

nonn

Author

Paul D. Hanna, Apr 03 2008

Status

approved