A138914 G.f. A(x) satisfies: 5*A(x) = A(A(A(A(x)))) + 4*x + x^2 with A(0)=0.

1, 1, 12, 390, 18304, 1071862, 73349996, 5661162666, 482252816998, 44704184452202, 4465265748489708, 477159108766899654, 54255973609630750372, 6536766146592886952548, 831617552461457925554152

Offset

1,3

Comments

A(A(A(A(x)))) is the 4th self-composition of the g.f. A(x).

Links

Table of n, a(n) for n=1..15.

Example

G.f.: A(x) = x + x^2 + 12*x^3 + 390*x^4 + 18304*x^5 + 1071862*x^6 +...
A(A(x)) = x + 2*x^2 + 26*x^3 + 841*x^4 + 39440*x^5 + 2308752*x^6 +...
A(A(A(x))) = x + 3*x^2 + 42*x^3 + 1359*x^4 + 63730*x^5 + 3730610*x^6 +...
A(A(A(A(x)))) = x + 4*x^2 + 60*x^3 + 1950*x^4 + 91520*x^5 + 5359310*x^6 +...
so that 5*A(x) = A(A(A(A(x)))) + 4*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, 4, G=subst(A, x, G+x*O(x^i))); A=A+polcoeff(G, i)*x^i); polcoeff(A, n))}

Crossrefs

Cf. A138739, A138913, A138915, A138916.

Sequence in context: A193132 A326214 A187513 * A326220 A308129 A356258

Adjacent sequences: A138911 A138912 A138913 * A138915 A138916 A138917

Keyword

nonn

Author

Paul D. Hanna, Apr 03 2008

Status

approved