A159608 - OEIS

%I #5 Aug 24 2017 09:19:21

%S 1,1,5,46,597,9791,191876,4348394,111561125,3192096511,100729014305,

%T 3474750994936,130094553648612,5254546985647116,227771218849108212,

%U 10548385893161367506,519835256567911242341,27164324421130818956039

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

%H Vaclav Kotesovec, <a href="/A159608/b159608.txt">Table of n, a(n) for n = 0..300</a>

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

%F a(n) ~ c * 3^n * n! * n^(1/3), where c = 0.242604467523310747298... - _Vaclav Kotesovec_, Aug 24 2017

%e G.f.: A(x) = 1 + x + 5*x^2 + 46*x^3 + 597*x^4 + 9791*x^5 +...

%e A(x)^3 = 1 + 3*x + 18*x^2 + 169*x^3 + 2157*x^4 + 34548*x^5 +...

%e log(1+x*A(x)^3) = x + 5*x^2/2 + 46*x^3/3 + 597*x^4/4 + 9791*x^5/5 +...

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

%Y Cf. variants: A159606, A159607.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 16 2009