OFFSET
0,3
COMMENTS
Limit a(n)/5^[n(n-1)/2] = 1.153465224918418179626705381295781...
EXAMPLE
G.f.: A(x) = 1 + x + 5*x^2 + 135*x^3 + 17635*x^4 + 11196380*x^5 +...
Related functions are defined by:
A(x) = 1 + x*B(x)^5;
B(x) = 1 + x*C(x)^25;
C(x) = 1 + x*D(x)^125;
D(x) = 1 + x*E(x)^625;
E(x) = 1 + x*F(x)^3125; ...
where the coefficients in the above functions begin:
B=[1,1,25,3425,2224175,7020109525,109933742396880,8592795153472287100,...];
C=[1,1,125,85875,278520875,4390379300750,343605429779453150,...];
D=[1,1,625,2148125,34827604375,2744338779394375,1073806035818802734500,...];
E=[1,1,3125,53709375,4353763021875,1715255710695800000,...];
F=[1,1,15625,1342765625,544228190109375,1072040316107238765625,...].
PROG
(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)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 17 2011
STATUS
approved