A212030 - OEIS

%I #6 Sep 03 2024 14:35:02

%S 1,1,3,18,142,1350,14607,174626,2263749,31426878,463144150,7199095692,

%T 117452998632,2003613768328,35628141598164,658723330672311,

%U 12636278430184303,251042922016657782,5156985005918404047,109382326645948764003,2392477607054828471286

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

%e G.f.: A(x) = 1 + x + 3*x^2 + 18*x^3 + 142*x^4 + 1350*x^5 + 14607*x^6 +...

%e Related expansions:

%e A(x)^2 = 1 + 2*x + 7*x^2 + 42*x^3 + 329*x^4 + 3092*x^5 + 33090*x^6 +...

%e A(x)^3 = 1 + 3*x + 12*x^2 + 73*x^3 + 570*x^4 + 5307*x^5 + 56226*x^6 +...

%e A(x*A(x)^2) = 1 + x + 5*x^2 + 37*x^3 + 346*x^4 + 3745*x^5 + 45132*x^6 +...

%e A(x*A(x)^2)^3 = 1 + 3*x + 18*x^2 + 142*x^3 + 1350*x^4 + 14607*x^5 +...

%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A^3, x, x*A^2)); polcoeff(A, n)}

%o for(n=0,30,print1(a(n),", "))

%Y Cf. A143508, A143501, A212029.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Apr 27 2012