A184577 - OEIS

%I #4 Mar 30 2012 18:37:25

%S 1,1,5,135,17635,11196380,35146865626,549810415675025,

%T 42966178319025765725,16784792206658535573353275,

%U 32783305434744311217446987595100,320150590803319511079060107920058643150

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

%C  Limit a(n)/5^[n(n-1)/2] = 1.153465224918418179626705381295781...

%e  G.f.: A(x) = 1 + x + 5*x^2 + 135*x^3 + 17635*x^4 + 11196380*x^5 +...

%e Related functions are defined by:

%e A(x) = 1 + x*B(x)^5;

%e B(x) = 1 + x*C(x)^25;

%e C(x) = 1 + x*D(x)^125;

%e D(x) = 1 + x*E(x)^625;

%e E(x) = 1 + x*F(x)^3125; ...

%e where the coefficients in the above functions begin:

%e B=[1,1,25,3425,2224175,7020109525,109933742396880,8592795153472287100,...];

%e C=[1,1,125,85875,278520875,4390379300750,343605429779453150,...];

%e D=[1,1,625,2148125,34827604375,2744338779394375,1073806035818802734500,...];

%e E=[1,1,3125,53709375,4353763021875,1715255710695800000,...];

%e F=[1,1,15625,1342765625,544228190109375,1072040316107238765625,...].

%o  (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  Cf. A120959, A184575, A184576.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jan 17 2011