A141380 G.f. satisfies: A(x) = x + A(A(A(A(x)^2))).

1, 1, 2, 8, 32, 138, 624, 2922, 14036, 68788, 342584, 1728812, 8820864, 45428616, 235846688, 1232970010, 6485204532, 34295308230, 182233431688, 972493015258, 5209848971700, 28008206873944, 151053157070944, 817032258098112

Offset

1,3

Links

Table of n, a(n) for n=1..24.

Formula

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

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 8*x^4 + 32*x^5 + 138*x^6 + 624*x^7 +...
Related expansions:
A(A(x)) = x + 2*x^2 + 6*x^3 + 27*x^4 + 134*x^5 + 706*x^6 + 3892*x^7 +...
A(A(A(A(x)))) = x + 4*x^2 + 20*x^3 + 122*x^4 + 820*x^5 + 5838*x^6 +...
A(A(A(A(x)^2))) = x^2 + 2*x^3 + 8*x^4 + 32*x^5 + 138*x^6 + 624*x^7 +...
The series reversion of A(x) = x - A(A(A(x^2))), where
A(A(A(x^2))) = x^2 + 3*x^4 + 12*x^6 + 63*x^8 + 368*x^10 + 2282*x^12 +...

Prog

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

Crossrefs

Cf. A141381, A141382, A141383; A141370.

Sequence in context: A308152 A150843 A150844 * A151304 A151828 A150845

Adjacent sequences: A141377 A141378 A141379 * A141381 A141382 A141383

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2008

Status

approved