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, 37275544492386193492506, 1879498672877297909667780, 99864380952380952380952380

Offset: 1

Author

Max Alekseyev, Feb 20 2010

Keywords

• nonn

Links

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

Crossrefs

Cf. A173500

Programs

Python

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

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). - Alex Ratushnyak, Aug 04 2012

Extensions

More terms from Michel Marcus, Apr 30 2025