A211824 G.f. satisfies: A(x) = 1 + x*( d/dx x*A(x) )^3.

1, 1, 6, 66, 1016, 19596, 447312, 11686008, 341966304, 11044539840, 389511815136, 14879686213728, 611795661826176, 26934556130346880, 1264203675152355840, 63023836596988857216, 3326204117173583906304, 185302040367551696870400, 10868134346437165639956480

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Formula

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

a(n) ~ c * 3^n * n! * n^(4/3), where c = 0.1005380575409567... - Vaclav Kotesovec, Aug 24 2017

Example

G.f.: A(x) = 1 + x + 6*x^2 + 66*x^3 + 1016*x^4 + 19596*x^5 + 447312*x^6 +...
Related expansions:
d/dx x*A(x) = 1 + 2*x + 18*x^2 + 264*x^3 + 5080*x^4 + 117576*x^5 +...
A'(x) = 1 + 12*x + 198*x^2 + 4064*x^3 + 97980*x^4 + 2683872*x^5 +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x*deriv(x*A)^3); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A112915, A211825, A211826.

Sequence in context: A371681 A216636 A169715 * A360976 A360236 A128319

Adjacent sequences: A211821 A211822 A211823 * A211825 A211826 A211827

Keyword

nonn

Author

Paul D. Hanna, Apr 21 2012

Status

approved