A173499 Number of sequences of length n with terms from {0,1,...,n-1} such that the sum of terms is 0 modulo n and the i-th term is not i.

0, 0, 2, 20, 204, 2604, 39990, 720600, 14913080, 348678440, 9090909090, 261535698060, 8230246567620, 281241170407092, 10371206370520814, 410525522232055664, 17361641481138401520, 781282469559318055056

Offset

1,3

Links

Table of n, a(n) for n=1..18.

ArtOfProblemSolving forum, 45th IMO Team Selection Test Lincoln, Nebraska

Formula

For odd n, a(n) = ((n-1)^n-n+1)/n.

For even n, a(n) = ((n-1)^n-1)/n.

a(n) = floor((n-1)^n / n). - From Alex Ratushnyak, Aug 04 2012.

Prog

(Python)
for n in range(1, 33):
    print((n-1)**n // n, end=', ')
# from Alex Ratushnyak, Aug 04 2012

Crossrefs

Cf. A173500

Sequence in context: A037729 A037624 A077327 * A067636 A226301 A000906

Adjacent sequences: A173496 A173497 A173498 * A173500 A173501 A173502

Keyword

nonn

Author

Max Alekseyev, Feb 20 2010

Status

approved