A141381 G.f. satisfies: A(x) = x + A(A(A(A(x))^2)).

1, 1, 4, 26, 202, 1786, 17296, 179826, 1980484, 22895120, 276005616, 3452880648, 44660161656, 595491975516, 8166748417744, 114983040461254, 1659471907641924, 24519436191927936, 370506958317854776

Offset

1,3

Links

Table of n, a(n) for n=1..19.

Formula

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

Example

G.f.: A(x) = x + x^2 + 4*x^3 + 26*x^4 + 202*x^5 + 1786*x^6 + 17296*x^7 +...
Related expansions:
A(A(x)) = x + 2*x^2 + 10*x^3 + 73*x^4 + 628*x^5 + 6038*x^6 + 62896*x^7 +...
A(A(A(x))) = x + 3*x^2 + 18*x^3 + 147*x^4 + 1392*x^5 + 14544*x^6 +...
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 + 4*x^3 + 26*x^4 + 202*x^5 + 1786*x^6 +...
The series reversion of A(x) = x - A(A(A(x)^2)), where
A(A(A(x)^2)) = x^2 + 2*x^3 + 11*x^4 + 68*x^5 + 526*x^6 + 4556*x^7 +...

Prog

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

Crossrefs

Cf. A141380, A141382, A141383; A141371.

Sequence in context: A369107 A368976 A253255 * A369124 A118971 A369102

Adjacent sequences: A141378 A141379 A141380 * A141382 A141383 A141384

Keyword

nonn

Author

Paul D. Hanna, Jun 28 2008

Status

approved