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
Keywords
Examples
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 +...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..250
Programs
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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),", "))
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