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A085606 (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 (list; graph; refs; listen; history; text; internal format)
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.

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 = {5,7,11,29,31,53,59,73,79,83,97,101,103,107,127,131,149,151,173,179,193,197,199,223,227,241,251,269,271,293,313,317,337,347,367,389,409,419,433,439,443,457,461,463,467,487,491,509,...}. p^2 divides a((p-1)/2) for prime p = {5,127,607}. - Alexander Adamchuk, Nov 13 2006

LINKS

Table of n, a(n) for n=0..19.

FORMULA

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

MATHEMATICA

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

CROSSREFS

Cf. A014293, A007778, A065440, A037205

Sequence in context: A222137 A115986 A295843 * A264691 A326223 A058785

Adjacent sequences:  A085603 A085604 A085605 * A085607 A085608 A085609

KEYWORD

sign

AUTHOR

Lekraj Beedassy, Jul 07 2003

EXTENSIONS

More terms from Ray Chandler, Nov 10 2003

STATUS

approved

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Last modified October 16 06:30 EDT 2019. Contains 328050 sequences. (Running on oeis4.)