A211828 G.f. satisfies: A(x) = x + x^2 * d/dx A(A(x)).

1, 1, 4, 30, 324, 4480, 74544, 1438808, 31459536, 766573668, 20569553080, 602290243456, 19105119410064, 652635503205608, 23888307843434944, 932847459551529600, 38716407912891973504, 1702050349577155752784, 79018450946973490981176

Offset

1,3

Links

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

Formula

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

Example

G.f.: A(x) = x + x^2 + 4*x^3 + 30*x^4 + 324*x^5 + 4480*x^6 + 74544*x^7 +...
Related expansions:
A'(x) = 1 + 2*x + 12*x^2 + 120*x^3 + 1620*x^4 + 26880*x^5 + 521808*x^6 +...
A(A(x)) = x + 2*x^2 + 10*x^3 + 81*x^4 + 896*x^5 + 12424*x^6 + 205544*x^7 +...

Prog

(PARI) {a(n)=local(A=x+x^2+x*O(x^n)); for(i=1, n, A=x+x^2*deriv(subst(A, x, A))); polcoeff(A, n)}
for(n=1, 21, print1(a(n), ", "))

Crossrefs

Cf. A211827.

Sequence in context: A367963 A180623 A128329 * A277759 A006149 A207833

Adjacent sequences: A211825 A211826 A211827 * A211829 A211830 A211831

Keyword

nonn

Author

Paul D. Hanna, Apr 21 2012

Status

approved