A141382 G.f. satisfies: A(x) = x + A(A(A(A(x)))^2).

1, 1, 6, 58, 702, 9830, 152632, 2565042, 45938878, 867667140, 17154629472, 353091007048, 7534733877540, 166160874412976, 3777158124019664, 88326122515058436, 2121170864722835600, 52242518805270485716

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Formula

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

Example

G.f.: A(x) = x + x^2 + 6*x^3 + 58*x^4 + 702*x^5 + 9830*x^6 +...
Related expansions:
A(A(x)) = x + 2*x^2 + 14*x^3 + 147*x^4 + 1890*x^5 + 27732*x^6 +...
A(A(A(x))) = x + 3*x^2 + 24*x^3 + 273*x^4 + 3730*x^5 + 57488*x^6 +...
A(A(A(A(x)))) = x + 4*x^2 + 36*x^3 + 442*x^4 + 6412*x^5 + 103890*x^6 +...
A(A(A(A(x)))^2) = x^2 + 6*x^3 + 58*x^4 + 702*x^5 + 9830*x^6 +...
The series reversion of A(x) = x - A(A(A(x))^2), where
A(A(A(x))^2) = x^2 + 4*x^3 + 33*x^4 + 358*x^5 + 4650*x^6 + 68168*x^7 +...

Prog

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

Crossrefs

Cf. A141380, A141381, A141383; A141371.

Sequence in context: A292574 A354228 A073848 * A212426 A259612 A305599

Adjacent sequences: A141379 A141380 A141381 * A141383 A141384 A141385

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2008

Status

approved