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A184577 G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^(5^n) )...)^125)^25)^5.

%I A184577 #7 Jun 30 2025 20:53:52
%S A184577 1,1,5,135,17635,11196380,35146865626,549810415675025,
%T A184577 42966178319025765725,16784792206658535573353275,
%U A184577 32783305434744311217446987595100,320150590803319511079060107920058643150
%N A184577 G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^(5^n) )...)^125)^25)^5.
%C A184577 Limit a(n)/5^[n(n-1)/2] = 1.153465224918418179626705381295781...
%e A184577 G.f.: A(x) = 1 + x + 5*x^2 + 135*x^3 + 17635*x^4 + 11196380*x^5 +...
%e A184577 Related functions are defined by:
%e A184577 A(x) = 1 + x*B(x)^5;
%e A184577 B(x) = 1 + x*C(x)^25;
%e A184577 C(x) = 1 + x*D(x)^125;
%e A184577 D(x) = 1 + x*E(x)^625;
%e A184577 E(x) = 1 + x*F(x)^3125; ...
%e A184577 where the coefficients in the above functions begin:
%e A184577 B=[1,1,25,3425,2224175,7020109525,109933742396880,8592795153472287100,...];
%e A184577 C=[1,1,125,85875,278520875,4390379300750,343605429779453150,...];
%e A184577 D=[1,1,625,2148125,34827604375,2744338779394375,1073806035818802734500,...];
%e A184577 E=[1,1,3125,53709375,4353763021875,1715255710695800000,...];
%e A184577 F=[1,1,15625,1342765625,544228190109375,1072040316107238765625,...].
%o A184577 (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(5^(n-j))); polcoeff(A, n)}
%Y A184577 Cf. A120959, A184575, A184576.
%K A184577 nonn
%O A184577 0,3
%A A184577 _Paul D. Hanna_, Jan 17 2011