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A085606
a(n) = (n-1)^n - 1.
7
0, -1, 0, 7, 80, 1023, 15624, 279935, 5764800, 134217727, 3486784400, 99999999999, 3138428376720, 106993205379071, 3937376385699288, 155568095557812223, 6568408355712890624, 295147905179352825855, 14063084452067724991008, 708235345355337676357631
OFFSET
0,4
COMMENTS
Sequence relates to the "monkey and coconut problem"(A014293) giving the number of coconuts received by each of the n sailors from the ultimate equitable distribution the next day.
From Alexander Adamchuk, Nov 13 2006: (Start)
4n^2 divides a(2n).
Odd prime p divides a(p-1).
8p^2 divides a(2p) for an odd prime p.
32p^4 divides a(2p^2) for an odd prime p.
64p^8 divides a(2p^4) for an odd prime p.
p^3 divides a(p^3+2) for prime p.
p divides a((p-1)/2) for prime p in A157437.
p^2 divides a((p-1)/2) for prime p = {5,127,607}. (End)
FORMULA
a(n) = A065440(n) - 1.
MATHEMATICA
Table[(n-1)^n-1, {n, 0, 30}] (* Alexander Adamchuk, Nov 13 2006 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Lekraj Beedassy, Jul 07 2003
EXTENSIONS
More terms from Ray Chandler, Nov 10 2003
STATUS
approved