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%I #6 Oct 11 2020 05:13:45
%S 1,1,6,66,1034,20790,507600,14546196,478095264,17722127700,
%T 731393039376,33262113690576,1652889277811448,89115877932595848,
%U 5181554275409183904,323216011162774715904,21531610593372148573824
%N G.f.: A(x) = 1+x*(1+2x*(1+3x*(...(1+n*x*(...)^3)^3...)^3)^3)^3.
%C (a(n)/n!)^(1/n) tends to 4.26315... - _Vaclav Kotesovec_, Oct 11 2020
%H Vaclav Kotesovec, <a href="/A128319/b128319.txt">Table of n, a(n) for n = 0..360</a>
%e G.f.: A(x) = 1 + x*B(x)^3; B(x) = 1 + 2*x*C(x)^3; C(x) = 1 + 3*x*D(x)^3; D(x) = 1 + 4*x*E(x)^3; E(x) = 1 + 5*x*F(x)^3; F(x) = 1 + 6*x*G(x)^3; ...
%e where the respective sequences begin:
%e A=[1,1,6,66,1034,20790,507600,14546196,478095264,...];
%e B=[1,2,18,270,5454,135936,3992544,134386344,5088220200,...];
%e C=[1,3,36,684,16932,504540,17367840,673851600,28994802120,...];
%e D=[1,4,60,1380,40460,1404000,55499040,2443032360,118003755960,...];
%e E=[1,5,90,2430,82350,3262770,145741680,7183818180,385393611960,...];
%e F=[1,6,126,3906,150234,6693120,333506880,18208871856,1075094932464,...];
%e G=[1,7,168,5880,253064,12523896,688855104,41282607744,2661610538160,..];
%e H=[1,8,216,8424,401112,21833280,1314118080,85783244400,5998813428240,..];
%o (PARI) {a(n)=local(A=1+(n+1)*x);for(k=0,n,A=1+(n-k+1)*x*A^3 +x*O(x^n));polcoeff(A,n)}
%Y Cf. A128318.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Mar 07 2007
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