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n^(n!) mod (n!)^n.
2

%I #12 Jan 13 2013 16:55:10

%S 0,0,0,81,225280,7991790625,1078848154238976,

%T 65180706714634067542224001,1650157594512930366268925848349310976,

%U 66807065275536807794426016376688705273224158387201

%N n^(n!) mod (n!)^n.

%F a(n) = A053986(n) mod A036740(n).

%e a(3) = 3^6 mod 6^3 = 729 mod 216 = 81.

%o (Python)

%o import math

%o for n in range(12):

%o f = math.factorial(n)

%o print (n**f) % (f**n),

%o (Maxima) A187751(n):=mod(n^(n!),(n!)^n)$ makelist(A187751(n),n,0,9); /* _Martin Ettl_, Jan 13 2013 */

%Y Cf. A053986, A036740.

%K nonn

%O 0,4

%A _Alex Ratushnyak_, Jan 03 2013