A085606 a(n) = (n-1)^n - 1.

0, -1, 0, 7, 80, 1023, 15624, 279935, 5764800, 134217727, 3486784400, 99999999999, 3138428376720, 106993205379071, 3937376385699288, 155568095557812223, 6568408355712890624, 295147905179352825855, 14063084452067724991008, 708235345355337676357631

Offset: 0

Author

Lekraj Beedassy, Jul 07 2003

Keywords

• sign

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)

Crossrefs

Cf. A014293, A007778, A065440, A037205, A157437.

Programs

Mathematica

Table[(n-1)^n-1,{n,0,30}] (* Alexander Adamchuk, Nov 13 2006 *)

Formula

a(n) = A065440(n) - 1.

Extensions

More terms from Ray Chandler, Nov 10 2003