A141383 G.f. satisfies: A(x) = x + A(A(A(A(x))))^2.

1, 1, 8, 104, 1724, 33280, 715308, 16683724, 415466708, 10926375108, 301131874516, 8648002744564, 257687247253732, 7940507243098200, 252374158974639744, 8255994209084399972, 277508512417717367138

Offset

1,3

Links

Table of n, a(n) for n=1..17.

Formula

G.f. satisfies: A( x - A(A(A(x)))^2 ) = x.

Example

G.f.: A(x) = x + x^2 + 8*x^3 + 104*x^4 + 1724*x^5 + 33280*x^6 +...
Related expansions:
A(A(x)) = x + 2*x^2 + 18*x^3 + 249*x^4 + 4304*x^5 + 85740*x^6 +...
A(A(A(x))) = x + 3*x^2 + 30*x^3 + 441*x^4 + 7958*x^5 + 163940*x^6 +...
A(A(A(A(x)))) = x + 4*x^2 + 44*x^3 + 686*x^4 + 12928*x^5 + 275758*x^6 +...
A(A(A(A(x))))^2 = x^2 + 8*x^3 + 104*x^4 + 1724*x^5 + 33280*x^6 +...
The series reversion of A(x) = x - A(A(A(x)))^2, where
A(A(A(x)))^2 = x^2 + 6*x^3 + 69*x^4 + 1062*x^5 + 19462*x^6 + 402088*x^7 +...

Prog

(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+subst(A^2, x, subst(A, x, subst(A, x, A+x*O(x^n))))); polcoeff(A, n)}

Crossrefs

Cf. A141380, A141381, A141382; A141372.

Sequence in context: A354064 A106260 A112121 * A034300 A266044 A359801

Adjacent sequences: A141380 A141381 A141382 * A141384 A141385 A141386

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2008

Status

approved