A232663 Number of permutations of order n such that no proper partial sum is zero modulo n.

1, 1, 2, 12, 48, 280, 2040, 16632, 139440, 1404864, 15405120, 185361792, 2380777344, 33252800256, 495338598144

Offset

1,3

Links

Table of n, a(n) for n=1..15.

K. Gaitanas, Avoiding multiples of p, MathOverflow.

Formula

For n>1, a(n) = A232664(n) * (n-1-(n mod 2)).

Example

For n=4, in permutation (1,2,4,3), proper partial sums are 1, 1+2=3, 1+2+4=7, neither of which is zero modulo n. The number of such permutations is a(4)=12.

Crossrefs

Sequence in context: A370696 A052569 A221663 * A052591 A029766 A088311

Adjacent sequences: A232660 A232661 A232662 * A232664 A232665 A232666

Keyword

nonn,more

Author

Max Alekseyev, Nov 27 2013

Status

approved