A218223 G.f. A(x) satisfies: A(x) = 1+x + x^2*[d/dx A(x)^3].

1, 1, 3, 24, 273, 3996, 70785, 1465506, 34662222, 921511944, 27201024639, 882828325530, 31253560065684, 1198758613494852, 49530067909218819, 2193498057583259784, 103664556373964098860, 5207896547115772335552, 277161367378578537506868

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..320

Formula

G.f. A(x) satisfies: A(x) = 1+x + 3*x^2*A(x)^2*A'(x).

a(n) ~ c * 3^n * n! / n^(1/3), where c = 0.3133426736012301024021... - Vaclav Kotesovec, Aug 24 2017

Example

G.f.: A(x) = 1 + x + 3*x^2 + 24*x^3 + 273*x^4 + 3996*x^5 + 70785*x^6 +...
Related series:
A(x)^3 = 1 + 3*x + 12*x^2 + 91*x^3 + 999*x^4 + 14157*x^5 + 244251*x^6 +...
d/dx A(x)^3 = 3 + 24*x + 273*x^2 + 3996*x^3 + 70785*x^4 + 1465506*x^5 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x+x^2*deriv(A^3+x*O(x^n))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A185183, A218224.

Sequence in context: A194957 A081133 A352278 * A276360 A354289 A351763

Adjacent sequences: A218220 A218221 A218222 * A218224 A218225 A218226

Keyword

nonn

Author

Paul D. Hanna, Oct 23 2012

Status

approved